1 Set Up

1.1 R Code

#packages we need for this code file
library(ggplot2)
library(mgcv)
library(lubridate)
library(zoo)
library(tidyverse)
library(dplyr)
library(DHARMa)
library(mgcViz)
library(extrafont)
library(arm)
loadfonts()
library(stargazer)
library(ellipse)
library(dotwhisker)
library(countreg)
#define functions we will need for analysis
#expit function
expit<-function(x){
  return(exp(x)/(1 + exp(x)))
}

#logit function
logit<-function(x){
  return(log(x/(1 - x)))
}

1.2 Data

#read in data
main_analysis_data<-read.csv("./Data/full_data_set_11_29_21_unintentional.csv")

################################## set up data set ################################
#add the intervention dates and time period data
main_analysis_data$Intervention_First_Date<-as.Date(main_analysis_data$Intervention_First_Date)
main_analysis_data$Time_Period_Start<-as.Date(main_analysis_data$Time_Period_Start)
names(main_analysis_data)[which(colnames(main_analysis_data) == "sum_deaths")] <- "imputed_deaths"

################################## set up the Regions ##############################
#set up the regions according to Census: https://www.census.gov/geographies/reference-maps/2010/geo/2010-census-regions-and-divisions-of-the-united-states.html
NE.name <- c("Connecticut","Maine","Massachusetts","New Hampshire",
             "Rhode Island","Vermont","New Jersey","New York",
             "Pennsylvania")

MW.name <- c("Indiana","Illinois","Michigan","Ohio","Wisconsin",
             "Iowa","Kansas","Minnesota","Missouri","Nebraska",
             "North Dakota","South Dakota")

S.name <- c("Delaware","District of Columbia","Florida","Georgia",
            "Maryland","North Carolina","South Carolina","Virginia",
            "West Virginia","Alabama","Kentucky","Mississippi",
            "Tennessee","Arkansas","Louisiana","Oklahoma","Texas")

W.name <- c("Arizona","Colorado","Idaho","New Mexico","Montana",
            "Utah","Nevada","Wyoming","Alaska","California",
            "Hawaii","Oregon","Washington")

region.list <- list(
  Northeast=NE.name,
  Midwest=MW.name,
  South=S.name,
  West=W.name)

#initialize vector with "West" and then impute the other regions for the states
main_analysis_data$Region<-rep("West", nrow(main_analysis_data))
for(state in unique(main_analysis_data$State)){
  if(state %in% region.list$Northeast){
    main_analysis_data$Region[main_analysis_data$State == state]<-"Northeast"
  }else if(state %in% region.list$Midwest){
    main_analysis_data$Region[main_analysis_data$State == state]<-"Midwest"
  }else if(state %in% region.list$South){
    main_analysis_data$Region[main_analysis_data$State == state]<-"South"
  }
}

2 Sandwich Estimator Code

#here, we estimate the variance-covariance matrix through the sandwich estimator
#we create a function so that we don't have to keep writing the code:
#cov_data is such that rows are state-time combinations and columns are the different policy measures
#coef_values need to be in order of the columns of cov_data
#z_value is the z-value that corresponds to the CI. We default to 95% CI so we default to 1.96
#we take p as the number of parametesr for a bias correction

compute_sd_and_CI <- function(cov_data, observed_y, coef_values, z_value = 1.96, p,
                              print_full_cov = FALSE){
  middle_term <- matrix(0, nrow = ncol(cov_data), ncol = ncol(cov_data))
  for(i in 1:nrow(cov_data)){
    #sum_{s,t} (z_{s,t}z_{s,t}^T)*(y_{s,t}-z_{s,t}^T theta)^2
    middle_term <- middle_term + tcrossprod(as.matrix(cov_data[i,]))*
      as.numeric((observed_y[i] - t(as.matrix(cov_data[i,]))%*%coef_values)^2)
  }
  #(Z^T Z)^{-1}*middle_term*(Z^T Z)^{-1}
  var_cov <- solve(crossprod(cov_data))%*%(middle_term)%*%solve(crossprod(cov_data))*(nrow(cov_data)/(nrow(cov_data) - p))
  #we obtain the standard deviations by taking the square root of the diagonal of the variance-covariance matrix.
  sd_of_coefficients <- sqrt(diag(var_cov))
  
  #find the CI for the coefficients
  lb_coef <- coef_values - z_value*(sd_of_coefficients)
  ub_coef <- coef_values + z_value*(sd_of_coefficients)
  
  return_data_set <- data.frame(lb_coef, coef_values, ub_coef, sd_coef = sd_of_coefficients)
  
  if(print_full_cov){
    return(list(return_data_set = return_data_set, var_cov = var_cov))
  }else{
    return(return_data_set)
  }
}

3 Attributable Deaths Computation

attr_death_compute <- function(data, coef_data, post_tx_model = TRUE, tx_name = NULL){
  attr_table <- data.frame(matrix(NA, nrow = unique(data$Time_Period_ID), ncol = 4)) 
  
  for(time in unique(data$Time_Period_ID)){
    #filter data to time period t
    time_data <- data %>%
      filter(Time_Period_ID == time)
    
    #obtain the population
    pop <- sum(time_data$population)
    
    #obtain the estimated probability had intervention not occurred
    if(post_tx_model == TRUE){
      est_prob_no_int <- exp(log(time_data$prop_dead) - apply(sapply(0:39, function(k){time_data[,paste("pos_", k, "_pd", sep = "")]*
          coef_data[paste("pos_", k, "_pd", sep = ""), "coef_values"]}), 1, sum))
    }else{
      est_prob_no_int <- exp(log(time_data$prop_dead) - time_data[tx_name]*coef_data[tx_name, "coef_values"])
    }
    
    #estimated number of OD had intervention not occurred
    n_od_no_int <- pop*est_prob_no_int
    
    #obtain LB
    if(post_tx_model == TRUE){
      est_prob_no_int_lb <- exp(log(time_data$prop_dead) - apply(sapply(0:39, function(k){time_data[,paste("pos_", k, "_pd", sep = "")]*
          coef_data[paste("pos_", k, "_pd", sep = ""), "lb_coef"]}), 1, sum))
    }else{
      est_prob_no_int_lb <- exp(log(time_data$prop_dead) - time_data[tx_name]*coef_data[tx_name, "lb_coef"])
    }
    n_od_no_int_lb <- pop*est_prob_no_int_lb
    
    #obtain UB
    if(post_tx_model == TRUE){
      est_prob_no_int_ub <- exp(log(time_data$prop_dead) - apply(sapply(0:39, function(k){time_data[,paste("pos_", k, "_pd", sep = "")]*
          coef_data[paste("pos_", k, "_pd", sep = ""), "ub_coef"]}), 1, sum))
    }else{
      est_prob_no_int_ub <- exp(log(time_data$prop_dead) - time_data[tx_name]*coef_data[tx_name, "ub_coef"])
    }
    n_od_no_int_ub <- pop*est_prob_no_int_ub

    
    attr_table[time,] <- c(time, sum(time_data$imputed_deaths) - sum(n_od_no_int), 
                        sum(time_data$imputed_deaths) - sum(n_od_no_int_lb), 
                        sum(time_data$imputed_deaths - n_od_no_int_ub))
    
    
  }
  colnames(attr_table) <- c("Time_Period", "attr_deaths", "attr_deaths_lb", "attr_deaths_ub")
  attr_table
}

4 Event Study Data Creation

main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population
#create the dataset for the event study to check for pre-trend analysis
time_data_int <- main_analysis_data %>%
  #group by the state
  group_by(State) %>%
  #find the time interval ID for the intervention time
  summarise(intervention_time_id = ifelse(floor_date(Intervention_First_Date, "6 months") == Time_Period_Start, Time_Period_ID, NA)) %>%
  #filter out the other time periods that aren't the intervention date
  filter(!is.na(intervention_time_id))

#merge the time_data_int with the main dataset
merged_main_time_data_int <- merge(main_analysis_data, time_data_int, by = "State", all.x = TRUE)

#create the columns that associate with the periods before the intervention
#the max number of periods before the intervention is determined by the maximum time period of the intervention
neg_periods_df <- sapply(1:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 1),
#the indicator for x periods before intervention is equal to 1 if the time ID of intervention minus time ID is equal to x
                         function(x){ifelse(merged_main_time_data_int$intervention_time_id - 
                                              merged_main_time_data_int$Time_Period_ID == x, 1, 0)})

#create the column names
colnames(neg_periods_df) <- sapply(1:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 1), 
                                   function(x){paste("neg_", x, "_pd", sep = "")})
#add in the state and time ID columns
neg_periods_df <- cbind(neg_periods_df, "State" = merged_main_time_data_int$State, 
                        "Time_Period_ID" = merged_main_time_data_int$Time_Period_ID)
#for Hawaii, impute a 0 because it is NA right now
neg_periods_df[neg_periods_df[,"State"] == "Hawaii", 1:34] <- 0

#create the columns that associate with the periods after the intervention
#the max number of periods after the intervention is determined by the maximum Time ID minus the minus time period of the intervention
#the period 0 is associated with intervention time
pos_periods_df <- sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                         function(x){ifelse(merged_main_time_data_int$Time_Period_ID - 
                                              merged_main_time_data_int$intervention_time_id == x, 1, 0)})
#create the column names
colnames(pos_periods_df) <- sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})
#add in the state and time ID columns
pos_periods_df <- cbind(pos_periods_df, "State" = merged_main_time_data_int$State, 
                        "Time_Period_ID" = merged_main_time_data_int$Time_Period_ID)
#for Hawaii, impute a 0 because it is NA right now
pos_periods_df[pos_periods_df[,"State"] == "Hawaii", 1:40] <- 0

#merge the columns of indicators for before and after the intervention with the main analysis data to create the dataset for event study
sensitivity_anlys_event_study_data <- merge(main_analysis_data, 
                                            neg_periods_df, by = c("State", "Time_Period_ID"))

sensitivity_anlys_event_study_data <- merge(sensitivity_anlys_event_study_data, 
                                            pos_periods_df, by = c("State", "Time_Period_ID"))
#change the indicator values to numeric type 
neg_1_index <- which(colnames(sensitivity_anlys_event_study_data) == "neg_1_pd")
pos_39_index <- which(colnames(sensitivity_anlys_event_study_data) == "pos_39_pd")

sensitivity_anlys_event_study_data[, neg_1_index:pos_39_index] <- apply(sensitivity_anlys_event_study_data[, neg_1_index:pos_39_index], 
                                                                      2, as.numeric)

5 OLS Model Main Analysis With Smoothed Time Effects

#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population

#fit an OLS with smoothed time effects
main_analysis_model<-gam(prop_dead~ State +
                           s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
                           Naloxone_Pharmacy_Yes_Redefined +
                           Naloxone_Pharmacy_No_Redefined +
                           Medical_Marijuana_Redefined +
                           Recreational_Marijuana_Redefined +
                           GSL_Redefined +
                           PDMP_Redefined +
                           Medicaid_Expansion_Redefined +
                           Intervention_Redefined ,
                         data = main_analysis_data)

summary(main_analysis_model)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## prop_dead ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     Intervention_Redefined
## 
## Parametric coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       7.018e-05  3.379e-06  20.769  < 2e-16 ***
## StateAlaska                       5.159e-06  4.759e-06   1.084 0.278444    
## StateArizona                      1.365e-05  4.334e-06   3.149 0.001663 ** 
## StateArkansas                    -2.699e-05  4.270e-06  -6.321 3.23e-10 ***
## StateCalifornia                  -1.708e-05  4.759e-06  -3.590 0.000339 ***
## StateColorado                    -4.307e-06  4.742e-06  -0.908 0.363951    
## StateConnecticut                  1.529e-05  4.538e-06   3.369 0.000770 ***
## StateDelaware                     2.394e-05  4.350e-06   5.504 4.21e-08 ***
## StateFlorida                      1.569e-05  4.273e-06   3.671 0.000248 ***
## StateGeorgia                     -6.789e-06  4.272e-06  -1.589 0.112221    
## StateHawaii                      -2.355e-05  4.668e-06  -5.044 4.98e-07 ***
## StateIdaho                       -7.124e-06  4.273e-06  -1.667 0.095614 .  
## StateIllinois                     5.370e-06  4.340e-06   1.237 0.216089    
## StateIndiana                      1.233e-05  4.245e-06   2.903 0.003732 ** 
## StateIowa                        -3.239e-05  4.259e-06  -7.604 4.46e-14 ***
## StateKansas                      -1.586e-05  4.227e-06  -3.752 0.000181 ***
## StateKentucky                     5.811e-05  4.273e-06  13.600  < 2e-16 ***
## StateLouisiana                    2.092e-05  4.221e-06   4.956 7.83e-07 ***
## StateMaine                        7.921e-06  4.727e-06   1.676 0.093956 .  
## StateMaryland                    -5.107e-05  4.337e-06 -11.776  < 2e-16 ***
## StateMassachusetts                2.091e-05  4.308e-06   4.854 1.30e-06 ***
## StateMichigan                     2.500e-06  4.375e-06   0.571 0.567859    
## StateMinnesota                   -3.845e-05  4.472e-06  -8.600  < 2e-16 ***
## StateMississippi                 -6.076e-06  4.223e-06  -1.439 0.150410    
## StateMissouri                     8.778e-06  4.368e-06   2.010 0.044589 *  
## StateMontana                     -3.177e-05  4.496e-06  -7.066 2.22e-12 ***
## StateNebraska                    -3.791e-05  4.293e-06  -8.830  < 2e-16 ***
## StateNevada                       2.944e-05  4.590e-06   6.414 1.78e-10 ***
## StateNew Hampshire                1.711e-05  4.296e-06   3.984 7.04e-05 ***
## StateNew Jersey                   6.741e-06  4.347e-06   1.551 0.121163    
## StateNew Mexico                   4.934e-05  4.667e-06  10.572  < 2e-16 ***
## StateNew York                    -8.681e-06  4.375e-06  -1.984 0.047351 *  
## StateNorth Carolina               1.214e-05  4.213e-06   2.882 0.003997 ** 
## StateNorth Dakota                -4.294e-05  4.251e-06 -10.099  < 2e-16 ***
## StateOhio                         4.302e-05  4.285e-06  10.040  < 2e-16 ***
## StateOklahoma                     3.167e-05  4.252e-06   7.448 1.43e-13 ***
## StateOregon                      -2.464e-05  4.725e-06  -5.214 2.04e-07 ***
## StatePennsylvania                 4.502e-05  4.277e-06  10.526  < 2e-16 ***
## StateRhode Island                 1.971e-05  4.438e-06   4.442 9.43e-06 ***
## StateSouth Carolina               1.255e-05  4.247e-06   2.955 0.003168 ** 
## StateSouth Dakota                -3.956e-05  4.272e-06  -9.260  < 2e-16 ***
## StateTennessee                    3.447e-05  4.201e-06   8.204 4.21e-16 ***
## StateTexas                       -5.506e-06  4.269e-06  -1.290 0.197270    
## StateUtah                         3.340e-06  4.226e-06   0.790 0.429480    
## StateVermont                     -1.370e-05  4.458e-06  -3.072 0.002153 ** 
## StateVirginia                    -3.785e-06  4.221e-06  -0.897 0.369967    
## StateWashington                  -6.966e-06  4.813e-06  -1.447 0.147995    
## StateWest Virginia                8.944e-05  4.274e-06  20.926  < 2e-16 ***
## StateWisconsin                   -1.498e-06  4.230e-06  -0.354 0.723299    
## StateWyoming                     -3.949e-08  4.225e-06  -0.009 0.992544    
## Naloxone_Pharmacy_Yes_Redefined  -4.614e-06  2.766e-06  -1.668 0.095477 .  
## Naloxone_Pharmacy_No_Redefined   -1.572e-06  2.472e-06  -0.636 0.524742    
## Medical_Marijuana_Redefined       1.229e-05  1.963e-06   6.259 4.76e-10 ***
## Recreational_Marijuana_Redefined -7.976e-06  3.125e-06  -2.552 0.010776 *  
## GSL_Redefined                     4.813e-06  2.023e-06   2.379 0.017465 *  
## PDMP_Redefined                   -1.394e-05  1.581e-06  -8.815  < 2e-16 ***
## Medicaid_Expansion_Redefined      1.307e-05  1.937e-06   6.744 2.03e-11 ***
## Intervention_Redefined            4.835e-07  1.558e-06   0.310 0.756359    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df     F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   6.359  7.493 50.65  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.045  8.752 78.69  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     7.759  8.600 78.15  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      3.471  4.324 49.80  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.831   Deviance explained = 83.8%
## GCV = 3.6721e-10  Scale est. = 3.5186e-10  n = 2000
gam.check(main_analysis_model, page = 1)

## 
## Method: GCV   Optimizer: magic
## Smoothing parameter selection converged after 4 iterations.
## The RMS GCV score gradient at convergence was 1.204512e-13 .
## The Hessian was positive definite.
## Model rank =  94 / 94 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                                k'  edf k-index p-value
## s(Time_Period_ID):as.factor(Region)Midwest   9.00 6.36     1.1       1
## s(Time_Period_ID):as.factor(Region)Northeast 9.00 8.04     1.1       1
## s(Time_Period_ID):as.factor(Region)South     9.00 7.76     1.1       1
## s(Time_Period_ID):as.factor(Region)West      9.00 3.47     1.1       1
#examine fitted values
summary(fitted(main_analysis_model))
##       Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
## -3.777e-05  4.117e-05  6.437e-05  6.974e-05  9.082e-05  2.257e-04
hist(fitted(main_analysis_model))

plot(main_analysis_model, pages = 1)

5.1 Coefficients and 95% CI

#compute the full dataset including basis functions
full_df_w_basis_functions <- as.matrix(data.frame(predict(main_analysis_model, type = "lpmatrix")))

#estimate the 95% CI and SD
coefficient_values <- coef(main_analysis_model)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci <- compute_sd_and_CI(full_df_w_basis_functions, main_analysis_data$prop_dead,
                                             coefficient_values, p = ncol(full_df_w_basis_functions) - 50)
main_analysis_sd_and_ci
##                                                      lb_coef   coef_values
## (Intercept)                                     6.550777e-05  7.018054e-05
## StateAlaska                                    -2.655990e-06  5.159359e-06
## StateArizona                                    8.125098e-06  1.364861e-05
## StateArkansas                                  -3.392878e-05 -2.699068e-05
## StateCalifornia                                -2.443119e-05 -1.708383e-05
## StateColorado                                  -1.101178e-05 -4.306558e-06
## StateConnecticut                                8.854097e-06  1.528886e-05
## StateDelaware                                   1.071282e-05  2.394408e-05
## StateFlorida                                    9.883990e-06  1.568719e-05
## StateGeorgia                                   -1.230845e-05 -6.788984e-06
## StateHawaii                                    -3.024143e-05 -2.354723e-05
## StateIdaho                                     -1.202074e-05 -7.124159e-06
## StateIllinois                                  -4.960886e-07  5.369827e-06
## StateIndiana                                    6.348464e-06  1.232618e-05
## StateIowa                                      -3.811363e-05 -3.238749e-05
## StateKansas                                    -2.087777e-05 -1.585840e-05
## StateKentucky                                   5.102376e-05  5.811102e-05
## StateLouisiana                                  1.523345e-05  2.091687e-05
## StateMaine                                      4.265523e-07  7.921034e-06
## StateMaryland                                  -5.872730e-05 -5.107340e-05
## StateMassachusetts                              1.387327e-05  2.091412e-05
## StateMichigan                                  -2.897250e-06  2.499546e-06
## StateMinnesota                                 -4.531672e-05 -3.845444e-05
## StateMississippi                               -1.277156e-05 -6.075702e-06
## StateMissouri                                   2.978337e-06  8.778322e-06
## StateMontana                                   -3.826259e-05 -3.177095e-05
## StateNebraska                                  -4.333837e-05 -3.790580e-05
## StateNevada                                     2.274149e-05  2.944268e-05
## StateNew Hampshire                              9.678361e-06  1.711410e-05
## StateNew Jersey                                -7.745525e-07  6.740960e-06
## StateNew Mexico                                 4.190804e-05  4.933843e-05
## StateNew York                                  -1.792963e-05 -8.681179e-06
## StateNorth Carolina                             7.689417e-06  1.214193e-05
## StateNorth Dakota                              -4.966876e-05 -4.293578e-05
## StateOhio                                       2.893621e-05  4.301557e-05
## StateOklahoma                                   2.355597e-05  3.166583e-05
## StateOregon                                    -3.120625e-05 -2.463765e-05
## StatePennsylvania                               3.866383e-05  4.501742e-05
## StateRhode Island                               1.070670e-05  1.971407e-05
## StateSouth Carolina                             7.769104e-06  1.254959e-05
## StateSouth Dakota                              -4.500751e-05 -3.955940e-05
## StateTennessee                                  2.853688e-05  3.446740e-05
## StateTexas                                     -1.335322e-05 -5.506353e-06
## StateUtah                                      -4.126413e-06  3.339770e-06
## StateVermont                                   -2.234625e-05 -1.369662e-05
## StateVirginia                                  -9.085845e-06 -3.784903e-06
## StateWashington                                -1.411732e-05 -6.965542e-06
## StateWest Virginia                              7.235479e-05  8.944156e-05
## StateWisconsin                                 -6.668206e-06 -1.497789e-06
## StateWyoming                                   -6.299542e-06 -3.948944e-08
## Naloxone_Pharmacy_Yes_Redefined                -1.014411e-05 -4.613656e-06
## Naloxone_Pharmacy_No_Redefined                 -5.737075e-06 -1.572452e-06
## Medical_Marijuana_Redefined                     7.611993e-06  1.228847e-05
## Recreational_Marijuana_Redefined               -1.323577e-05 -7.975570e-06
## GSL_Redefined                                   8.576557e-07  4.812567e-06
## PDMP_Redefined                                 -1.700621e-05 -1.394153e-05
## Medicaid_Expansion_Redefined                    8.785126e-06  1.306529e-05
## Intervention_Redefined                         -2.710819e-06  4.835333e-07
## s(Time_Period_ID):as.factor(Region)Midwest.1   -2.716312e-05 -2.061983e-05
## s(Time_Period_ID):as.factor(Region)Midwest.2   -1.886956e-05 -1.405098e-05
## s(Time_Period_ID):as.factor(Region)Midwest.3   -6.335372e-06 -2.063002e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4    1.639853e-06  6.425491e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5    9.341242e-06  1.336075e-05
## s(Time_Period_ID):as.factor(Region)Midwest.6    1.627683e-05  2.073943e-05
## s(Time_Period_ID):as.factor(Region)Midwest.7    2.697822e-05  3.314070e-05
## s(Time_Period_ID):as.factor(Region)Midwest.8    4.256399e-05  5.232296e-05
## s(Time_Period_ID):as.factor(Region)Midwest.9    3.704131e-05  4.985907e-05
## s(Time_Period_ID):as.factor(Region)Northeast.1 -3.492814e-05 -2.690368e-05
## s(Time_Period_ID):as.factor(Region)Northeast.2 -2.795223e-05 -2.145908e-05
## s(Time_Period_ID):as.factor(Region)Northeast.3 -5.668466e-06  5.052780e-07
## s(Time_Period_ID):as.factor(Region)Northeast.4 -5.787646e-06 -4.993248e-08
## s(Time_Period_ID):as.factor(Region)Northeast.5 -4.689682e-06  1.391242e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6  6.329001e-06  1.294496e-05
## s(Time_Period_ID):as.factor(Region)Northeast.7  3.867293e-05  4.828531e-05
## s(Time_Period_ID):as.factor(Region)Northeast.8  8.539287e-05  9.629882e-05
## s(Time_Period_ID):as.factor(Region)Northeast.9  6.552090e-05  8.026878e-05
## s(Time_Period_ID):as.factor(Region)South.1     -3.022522e-05 -2.337861e-05
## s(Time_Period_ID):as.factor(Region)South.2     -1.719691e-05 -1.253656e-05
## s(Time_Period_ID):as.factor(Region)South.3     -1.858526e-06  3.729042e-06
## s(Time_Period_ID):as.factor(Region)South.4      5.410765e-06  1.112647e-05
## s(Time_Period_ID):as.factor(Region)South.5      1.594179e-05  2.101759e-05
## s(Time_Period_ID):as.factor(Region)South.6      1.959869e-05  2.481184e-05
## s(Time_Period_ID):as.factor(Region)South.7      3.401158e-05  4.039071e-05
## s(Time_Period_ID):as.factor(Region)South.8      5.858355e-05  6.897540e-05
## s(Time_Period_ID):as.factor(Region)South.9      4.412813e-05  6.040295e-05
## s(Time_Period_ID):as.factor(Region)West.1      -1.869797e-05 -1.440514e-05
## s(Time_Period_ID):as.factor(Region)West.2      -9.832141e-06 -6.268216e-06
## s(Time_Period_ID):as.factor(Region)West.3      -3.690218e-07  3.701112e-06
## s(Time_Period_ID):as.factor(Region)West.4       8.175889e-06  1.186207e-05
## s(Time_Period_ID):as.factor(Region)West.5       1.340384e-05  1.734734e-05
## s(Time_Period_ID):as.factor(Region)West.6       1.665064e-05  2.108933e-05
## s(Time_Period_ID):as.factor(Region)West.7       1.896157e-05  2.437395e-05
## s(Time_Period_ID):as.factor(Region)West.8       2.439385e-05  3.137238e-05
## s(Time_Period_ID):as.factor(Region)West.9       2.428297e-05  3.186887e-05
##                                                      ub_coef      sd_coef
## (Intercept)                                     7.485331e-05 2.384067e-06
## StateAlaska                                     1.297471e-05 3.987423e-06
## StateArizona                                    1.917213e-05 2.818121e-06
## StateArkansas                                  -2.005259e-05 3.539844e-06
## StateCalifornia                                -9.736475e-06 3.748651e-06
## StateColorado                                   2.398666e-06 3.421033e-06
## StateConnecticut                                2.172362e-05 3.283042e-06
## StateDelaware                                   3.717534e-05 6.750643e-06
## StateFlorida                                    2.149038e-05 2.960814e-06
## StateGeorgia                                   -1.269519e-06 2.816053e-06
## StateHawaii                                    -1.685303e-05 3.415408e-06
## StateIdaho                                     -2.227577e-06 2.498256e-06
## StateIllinois                                   1.123574e-05 2.992814e-06
## StateIndiana                                    1.830390e-05 3.049856e-06
## StateIowa                                      -2.666136e-05 2.921497e-06
## StateKansas                                    -1.083903e-05 2.560905e-06
## StateKentucky                                   6.519828e-05 3.615948e-06
## StateLouisiana                                  2.660028e-05 2.899703e-06
## StateMaine                                      1.541551e-05 3.823715e-06
## StateMaryland                                  -4.341950e-05 3.905053e-06
## StateMassachusetts                              2.795498e-05 3.592274e-06
## StateMichigan                                   7.896342e-06 2.753467e-06
## StateMinnesota                                 -3.159217e-05 3.501162e-06
## StateMississippi                                6.201522e-07 3.416252e-06
## StateMissouri                                   1.457831e-05 2.959176e-06
## StateMontana                                   -2.527930e-05 3.312066e-06
## StateNebraska                                  -3.247323e-05 2.771721e-06
## StateNevada                                     3.614387e-05 3.418975e-06
## StateNew Hampshire                              2.454984e-05 3.793744e-06
## StateNew Jersey                                 1.425647e-05 3.834445e-06
## StateNew Mexico                                 5.676881e-05 3.791013e-06
## StateNew York                                   5.672703e-07 4.718596e-06
## StateNorth Carolina                             1.659443e-05 2.271688e-06
## StateNorth Dakota                              -3.620281e-05 3.435192e-06
## StateOhio                                       5.709492e-05 7.183345e-06
## StateOklahoma                                   3.977569e-05 4.137683e-06
## StateOregon                                    -1.806905e-05 3.351325e-06
## StatePennsylvania                               5.137102e-05 3.241630e-06
## StateRhode Island                               2.872143e-05 4.595593e-06
## StateSouth Carolina                             1.733007e-05 2.439021e-06
## StateSouth Dakota                              -3.411129e-05 2.779648e-06
## StateTennessee                                  4.039793e-05 3.025776e-06
## StateTexas                                      2.340510e-06 4.003501e-06
## StateUtah                                       1.080595e-05 3.809277e-06
## StateVermont                                   -5.046981e-06 4.413079e-06
## StateVirginia                                   1.516039e-06 2.704562e-06
## StateWashington                                 1.862399e-07 3.648868e-06
## StateWest Virginia                              1.065283e-04 8.717742e-06
## StateWisconsin                                  3.672628e-06 2.637968e-06
## StateWyoming                                    6.220563e-06 3.193904e-06
## Naloxone_Pharmacy_Yes_Redefined                 9.167953e-07 2.821659e-06
## Naloxone_Pharmacy_No_Redefined                  2.592170e-06 2.124808e-06
## Medical_Marijuana_Redefined                     1.696495e-05 2.385958e-06
## Recreational_Marijuana_Redefined               -2.715372e-06 2.683774e-06
## GSL_Redefined                                   8.767479e-06 2.017812e-06
## PDMP_Redefined                                 -1.087685e-05 1.563614e-06
## Medicaid_Expansion_Redefined                    1.734545e-05 2.183756e-06
## Intervention_Redefined                          3.677886e-06 1.629772e-06
## s(Time_Period_ID):as.factor(Region)Midwest.1   -1.407655e-05 3.338411e-06
## s(Time_Period_ID):as.factor(Region)Midwest.2   -9.232397e-06 2.458461e-06
## s(Time_Period_ID):as.factor(Region)Midwest.3    2.209367e-06 2.179781e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4    1.121113e-05 2.441652e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5    1.738026e-05 2.050771e-06
## s(Time_Period_ID):as.factor(Region)Midwest.6    2.520204e-05 2.276838e-06
## s(Time_Period_ID):as.factor(Region)Midwest.7    3.930318e-05 3.144121e-06
## s(Time_Period_ID):as.factor(Region)Midwest.8    6.208194e-05 4.979071e-06
## s(Time_Period_ID):as.factor(Region)Midwest.9    6.267683e-05 6.539674e-06
## s(Time_Period_ID):as.factor(Region)Northeast.1 -1.887921e-05 4.094113e-06
## s(Time_Period_ID):as.factor(Region)Northeast.2 -1.496592e-05 3.312834e-06
## s(Time_Period_ID):as.factor(Region)Northeast.3  6.679022e-06 3.149869e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4  5.687781e-06 2.927405e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5  7.472166e-06 3.102512e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6  1.956092e-05 3.375488e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7  5.789768e-05 4.904272e-06
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.072048e-04 5.564261e-06
## s(Time_Period_ID):as.factor(Region)Northeast.9  9.501667e-05 7.524432e-06
## s(Time_Period_ID):as.factor(Region)South.1     -1.653200e-05 3.493167e-06
## s(Time_Period_ID):as.factor(Region)South.2     -7.876207e-06 2.377730e-06
## s(Time_Period_ID):as.factor(Region)South.3      9.316611e-06 2.850800e-06
## s(Time_Period_ID):as.factor(Region)South.4      1.684217e-05 2.916176e-06
## s(Time_Period_ID):as.factor(Region)South.5      2.609339e-05 2.589692e-06
## s(Time_Period_ID):as.factor(Region)South.6      3.002500e-05 2.659775e-06
## s(Time_Period_ID):as.factor(Region)South.7      4.676984e-05 3.254660e-06
## s(Time_Period_ID):as.factor(Region)South.8      7.936725e-05 5.301965e-06
## s(Time_Period_ID):as.factor(Region)South.9      7.667777e-05 8.303480e-06
## s(Time_Period_ID):as.factor(Region)West.1      -1.011232e-05 2.190216e-06
## s(Time_Period_ID):as.factor(Region)West.2      -2.704291e-06 1.818329e-06
## s(Time_Period_ID):as.factor(Region)West.3       7.771245e-06 2.076599e-06
## s(Time_Period_ID):as.factor(Region)West.4       1.554826e-05 1.880707e-06
## s(Time_Period_ID):as.factor(Region)West.5       2.129085e-05 2.011993e-06
## s(Time_Period_ID):as.factor(Region)West.6       2.552802e-05 2.264638e-06
## s(Time_Period_ID):as.factor(Region)West.7       2.978632e-05 2.761414e-06
## s(Time_Period_ID):as.factor(Region)West.8       3.835090e-05 3.560473e-06
## s(Time_Period_ID):as.factor(Region)West.9       3.945476e-05 3.870355e-06

5.2 Event Study

5.2.1 Model Fitting

#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures, 
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention

formula_event_study <- formula(paste("prop_dead ~ State +
                                           s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2), 
                                            function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
                                     "+",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model<-gam(formula_event_study,
                                         data = sensitivity_anlys_event_study_data)

summary(sensitivity_anlys_event_study_model)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## prop_dead ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     neg_2_pd + neg_3_pd + neg_4_pd + neg_5_pd + neg_6_pd + neg_7_pd + 
##     neg_8_pd + neg_9_pd + neg_10_pd + neg_11_pd + neg_12_pd + 
##     neg_13_pd + neg_14_pd + neg_15_pd + neg_16_pd + neg_17_pd + 
##     neg_18_pd + neg_19_pd + neg_20_pd + neg_21_pd + neg_22_pd + 
##     neg_23_pd + neg_24_pd + neg_25_pd + neg_26_pd + neg_27_pd + 
##     neg_28_pd + neg_29_pd + neg_30_pd + neg_31_pd + neg_32_pd + 
##     neg_33_pd + pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + 
##     pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + 
##     pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + 
##     pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + 
##     pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + 
##     pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd + 
##     pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd + 
##     pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd
## 
## Parametric coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       7.588e-05  4.354e-06  17.428  < 2e-16 ***
## StateAlaska                       1.166e-05  6.301e-06   1.850 0.064426 .  
## StateArizona                      1.775e-05  4.846e-06   3.663 0.000256 ***
## StateArkansas                    -2.462e-05  4.547e-06  -5.414 6.98e-08 ***
## StateCalifornia                  -1.897e-05  5.581e-06  -3.399 0.000692 ***
## StateColorado                    -2.222e-07  5.135e-06  -0.043 0.965483    
## StateConnecticut                  1.530e-05  4.506e-06   3.395 0.000700 ***
## StateDelaware                     2.987e-05  6.004e-06   4.975 7.14e-07 ***
## StateFlorida                      1.139e-05  5.493e-06   2.073 0.038323 *  
## StateGeorgia                     -1.240e-05  5.864e-06  -2.115 0.034548 *  
## StateHawaii                      -2.639e-05  5.451e-06  -4.841 1.40e-06 ***
## StateIdaho                       -9.651e-07  5.658e-06  -0.171 0.864578    
## StateIllinois                     2.603e-06  5.048e-06   0.516 0.606170    
## StateIndiana                      1.431e-05  4.325e-06   3.308 0.000957 ***
## StateIowa                        -3.365e-05  4.593e-06  -7.326 3.52e-13 ***
## StateKansas                      -1.609e-05  4.200e-06  -3.830 0.000132 ***
## StateKentucky                     6.135e-05  4.579e-06  13.399  < 2e-16 ***
## StateLouisiana                    1.894e-05  4.647e-06   4.076 4.78e-05 ***
## StateMaine                        1.067e-05  4.767e-06   2.237 0.025374 *  
## StateMaryland                    -5.506e-05  5.120e-06 -10.754  < 2e-16 ***
## StateMassachusetts                2.174e-05  4.272e-06   5.088 3.98e-07 ***
## StateMichigan                     2.888e-06  4.488e-06   0.644 0.519936    
## StateMinnesota                   -3.812e-05  4.445e-06  -8.577  < 2e-16 ***
## StateMississippi                 -1.315e-06  5.276e-06  -0.249 0.803243    
## StateMissouri                     6.589e-06  4.545e-06   1.450 0.147278    
## StateMontana                     -3.305e-05  4.868e-06  -6.790 1.51e-11 ***
## StateNebraska                    -3.434e-05  4.888e-06  -7.026 2.98e-12 ***
## StateNevada                       3.027e-05  4.674e-06   6.476 1.20e-10 ***
## StateNew Hampshire                1.837e-05  4.365e-06   4.208 2.69e-05 ***
## StateNew Jersey                   3.449e-06  5.099e-06   0.676 0.498916    
## StateNew Mexico                   5.124e-05  4.758e-06  10.771  < 2e-16 ***
## StateNew York                    -8.375e-06  4.344e-06  -1.928 0.054035 .  
## StateNorth Carolina               1.088e-05  4.432e-06   2.454 0.014211 *  
## StateNorth Dakota                -3.894e-05  4.869e-06  -7.999 2.20e-15 ***
## StateOhio                         3.830e-05  5.855e-06   6.541 7.88e-11 ***
## StateOklahoma                     3.502e-05  4.498e-06   7.786 1.15e-14 ***
## StateOregon                      -2.245e-05  4.797e-06  -4.680 3.07e-06 ***
## StatePennsylvania                 4.174e-05  5.463e-06   7.640 3.47e-14 ***
## StateRhode Island                 2.541e-05  5.382e-06   4.722 2.51e-06 ***
## StateSouth Carolina               1.841e-05  5.762e-06   3.196 0.001418 ** 
## StateSouth Dakota                -3.379e-05  5.961e-06  -5.668 1.67e-08 ***
## StateTennessee                    3.470e-05  4.162e-06   8.336  < 2e-16 ***
## StateTexas                       -8.210e-06  5.292e-06  -1.551 0.121017    
## StateUtah                         2.925e-06  4.357e-06   0.671 0.502135    
## StateVermont                     -1.178e-05  4.512e-06  -2.611 0.009099 ** 
## StateVirginia                    -5.799e-06  4.732e-06  -1.225 0.220576    
## StateWashington                  -5.644e-06  4.809e-06  -1.174 0.240692    
## StateWest Virginia                9.400e-05  4.909e-06  19.151  < 2e-16 ***
## StateWisconsin                   -3.846e-06  4.659e-06  -0.826 0.409194    
## StateWyoming                      1.701e-06  4.259e-06   0.399 0.689636    
## Naloxone_Pharmacy_Yes_Redefined  -4.335e-06  2.768e-06  -1.566 0.117412    
## Naloxone_Pharmacy_No_Redefined   -1.607e-06  2.476e-06  -0.649 0.516370    
## Medical_Marijuana_Redefined       1.095e-05  1.987e-06   5.510 4.10e-08 ***
## Recreational_Marijuana_Redefined -8.742e-06  3.156e-06  -2.770 0.005667 ** 
## GSL_Redefined                     6.151e-06  2.023e-06   3.041 0.002394 ** 
## PDMP_Redefined                   -1.595e-05  1.601e-06  -9.961  < 2e-16 ***
## Medicaid_Expansion_Redefined      1.342e-05  1.958e-06   6.852 9.89e-12 ***
## neg_2_pd                         -4.444e-07  3.819e-06  -0.116 0.907376    
## neg_3_pd                          2.553e-07  3.881e-06   0.066 0.947557    
## neg_4_pd                         -3.100e-06  3.967e-06  -0.781 0.434610    
## neg_5_pd                         -5.533e-06  4.018e-06  -1.377 0.168666    
## neg_6_pd                         -5.831e-06  4.157e-06  -1.403 0.160816    
## neg_7_pd                         -9.095e-06  4.228e-06  -2.151 0.031609 *  
## neg_8_pd                         -1.185e-05  4.333e-06  -2.735 0.006290 ** 
## neg_9_pd                         -8.193e-06  4.513e-06  -1.815 0.069618 .  
## neg_10_pd                        -8.270e-06  4.643e-06  -1.781 0.075075 .  
## neg_11_pd                        -9.350e-06  4.789e-06  -1.952 0.051071 .  
## neg_12_pd                        -5.952e-06  5.068e-06  -1.174 0.240420    
## neg_13_pd                        -9.391e-06  5.195e-06  -1.808 0.070823 .  
## neg_14_pd                        -1.067e-05  5.329e-06  -2.003 0.045343 *  
## neg_15_pd                        -1.488e-05  5.477e-06  -2.716 0.006665 ** 
## neg_16_pd                        -1.449e-05  5.753e-06  -2.518 0.011884 *  
## neg_17_pd                        -1.773e-05  6.081e-06  -2.915 0.003600 ** 
## neg_18_pd                        -1.867e-05  6.299e-06  -2.964 0.003079 ** 
## neg_19_pd                        -1.932e-05  6.505e-06  -2.970 0.003015 ** 
## neg_20_pd                        -2.166e-05  6.879e-06  -3.149 0.001667 ** 
## neg_21_pd                        -2.102e-05  7.336e-06  -2.865 0.004215 ** 
## neg_22_pd                        -2.126e-05  7.508e-06  -2.832 0.004678 ** 
## neg_23_pd                        -1.875e-05  7.773e-06  -2.412 0.015962 *  
## neg_24_pd                        -2.300e-05  8.341e-06  -2.758 0.005876 ** 
## neg_25_pd                        -2.053e-05  8.492e-06  -2.417 0.015739 *  
## neg_26_pd                        -1.630e-05  8.858e-06  -1.841 0.065848 .  
## neg_27_pd                        -1.569e-05  9.861e-06  -1.591 0.111775    
## neg_28_pd                        -1.508e-05  1.003e-05  -1.503 0.132989    
## neg_29_pd                        -1.225e-05  1.059e-05  -1.157 0.247534    
## neg_30_pd                        -1.690e-05  1.126e-05  -1.501 0.133548    
## neg_31_pd                        -1.853e-05  1.142e-05  -1.623 0.104834    
## neg_32_pd                        -1.878e-05  1.239e-05  -1.515 0.129881    
## neg_33_pd                        -1.241e-05  1.572e-05  -0.789 0.430066    
## pos_0_pd                          2.540e-08  3.802e-06   0.007 0.994671    
## pos_1_pd                         -1.353e-06  3.842e-06  -0.352 0.724804    
## pos_2_pd                          1.645e-06  3.896e-06   0.422 0.673011    
## pos_3_pd                         -9.337e-09  3.966e-06  -0.002 0.998122    
## pos_4_pd                          5.733e-07  4.046e-06   0.142 0.887347    
## pos_5_pd                         -1.838e-06  4.140e-06  -0.444 0.657198    
## pos_6_pd                          2.345e-07  4.255e-06   0.055 0.956048    
## pos_7_pd                         -5.369e-07  4.380e-06  -0.123 0.902451    
## pos_8_pd                         -1.869e-06  4.543e-06  -0.411 0.680860    
## pos_9_pd                         -3.141e-06  4.696e-06  -0.669 0.503773    
## pos_10_pd                        -3.393e-06  4.831e-06  -0.702 0.482512    
## pos_11_pd                        -3.053e-06  4.997e-06  -0.611 0.541318    
## pos_12_pd                        -2.000e-06  5.172e-06  -0.387 0.699080    
## pos_13_pd                        -5.156e-06  5.332e-06  -0.967 0.333701    
## pos_14_pd                        -3.669e-06  5.558e-06  -0.660 0.509167    
## pos_15_pd                        -5.162e-06  5.766e-06  -0.895 0.370752    
## pos_16_pd                        -6.156e-06  5.952e-06  -1.034 0.301138    
## pos_17_pd                        -4.156e-06  6.195e-06  -0.671 0.502457    
## pos_18_pd                        -3.494e-06  6.410e-06  -0.545 0.585741    
## pos_19_pd                        -2.675e-06  6.587e-06  -0.406 0.684710    
## pos_20_pd                        -3.948e-06  6.860e-06  -0.576 0.564969    
## pos_21_pd                        -4.241e-06  7.134e-06  -0.594 0.552288    
## pos_22_pd                        -1.785e-06  7.359e-06  -0.243 0.808345    
## pos_23_pd                        -8.797e-07  7.620e-06  -0.115 0.908101    
## pos_24_pd                        -4.155e-06  7.956e-06  -0.522 0.601536    
## pos_25_pd                        -1.945e-06  8.292e-06  -0.235 0.814587    
## pos_26_pd                        -1.574e-06  8.490e-06  -0.185 0.852925    
## pos_27_pd                        -4.658e-06  8.717e-06  -0.534 0.593175    
## pos_28_pd                        -1.813e-06  8.911e-06  -0.203 0.838777    
## pos_29_pd                        -5.020e-06  9.380e-06  -0.535 0.592574    
## pos_30_pd                         4.239e-07  9.670e-06   0.044 0.965035    
## pos_31_pd                         1.238e-05  1.000e-05   1.237 0.216165    
## pos_32_pd                         1.023e-05  1.064e-05   0.961 0.336454    
## pos_33_pd                         9.607e-06  1.104e-05   0.870 0.384190    
## pos_34_pd                         1.713e-05  1.125e-05   1.524 0.127800    
## pos_35_pd                         2.667e-06  1.228e-05   0.217 0.828168    
## pos_36_pd                        -1.436e-06  1.249e-05  -0.115 0.908516    
## pos_37_pd                         1.587e-05  1.391e-05   1.141 0.253901    
## pos_38_pd                         1.614e-05  1.694e-05   0.952 0.340977    
## pos_39_pd                         2.397e-05  1.720e-05   1.394 0.163614    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df      F  p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   6.802  7.892  8.249  < 2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 7.971  8.719 33.756  < 2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     7.760  8.601 13.645  < 2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      3.218  4.023  8.800 9.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.834   Deviance explained = 84.7%
## GCV = 3.7432e-10  Scale est. = 3.4535e-10  n = 2000

5.2.2 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study <- data.frame(predict(sensitivity_anlys_event_study_model, type = "lpmatrix"))

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study <- coef(sensitivity_anlys_event_study_model)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci <- compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_event_study), 
                                                             sensitivity_anlys_event_study_data$prop_dead,
                                                             coefficient_values_sensitivity_anlys_event_study,
                                                             p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study) - 50)
(sensitivity_anlys_event_study_sd_and_ci)
##                                                      lb_coef   coef_values
## (Intercept)                                     7.018758e-05  7.588153e-05
## StateAlaska                                     2.702969e-06  1.165915e-05
## StateArizona                                    1.155015e-05  1.775014e-05
## StateArkansas                                  -3.147916e-05 -2.461562e-05
## StateCalifornia                                -2.621282e-05 -1.896949e-05
## StateColorado                                  -7.373523e-06 -2.222402e-07
## StateConnecticut                                9.001384e-06  1.529978e-05
## StateDelaware                                   1.674016e-05  2.986929e-05
## StateFlorida                                    4.837064e-06  1.138546e-05
## StateGeorgia                                   -1.962541e-05 -1.240243e-05
## StateHawaii                                    -3.362101e-05 -2.638682e-05
## StateIdaho                                     -7.178603e-06 -9.651171e-07
## StateIllinois                                  -3.493598e-06  2.602818e-06
## StateIndiana                                    8.595625e-06  1.430953e-05
## StateIowa                                      -3.926947e-05 -3.365310e-05
## StateKansas                                    -2.077318e-05 -1.608743e-05
## StateKentucky                                   5.467657e-05  6.134916e-05
## StateLouisiana                                  1.307945e-05  1.894281e-05
## StateMaine                                      3.064209e-06  1.066642e-05
## StateMaryland                                  -6.264271e-05 -5.505916e-05
## StateMassachusetts                              1.487224e-05  2.173840e-05
## StateMichigan                                  -2.245238e-06  2.888378e-06
## StateMinnesota                                 -4.470511e-05 -3.811967e-05
## StateMississippi                               -9.373824e-06 -1.314824e-06
## StateMissouri                                   4.649449e-07  6.589117e-06
## StateMontana                                   -3.912099e-05 -3.305272e-05
## StateNebraska                                  -4.052068e-05 -3.434330e-05
## StateNevada                                     2.390005e-05  3.026966e-05
## StateNew Hampshire                              1.079763e-05  1.836949e-05
## StateNew Jersey                                -3.652057e-06  3.448585e-06
## StateNew Mexico                                 4.384943e-05  5.124463e-05
## StateNew York                                  -1.732233e-05 -8.374509e-06
## StateNorth Carolina                             6.264255e-06  1.087630e-05
## StateNorth Dakota                              -4.679897e-05 -3.894169e-05
## StateOhio                                       2.420983e-05  3.829869e-05
## StateOklahoma                                   2.743480e-05  3.501696e-05
## StateOregon                                    -2.899092e-05 -2.245349e-05
## StatePennsylvania                               3.492330e-05  4.174037e-05
## StateRhode Island                               1.662438e-05  2.541168e-05
## StateSouth Carolina                             1.218258e-05  1.841450e-05
## StateSouth Dakota                              -4.078667e-05 -3.378823e-05
## StateTennessee                                  2.847526e-05  3.469856e-05
## StateTexas                                     -1.628838e-05 -8.209918e-06
## StateUtah                                      -5.184532e-06  2.924894e-06
## StateVermont                                   -2.046081e-05 -1.178060e-05
## StateVirginia                                  -1.101404e-05 -5.799118e-06
## StateWashington                                -1.264762e-05 -5.643995e-06
## StateWest Virginia                              7.736240e-05  9.400384e-05
## StateWisconsin                                 -9.701198e-06 -3.846319e-06
## StateWyoming                                   -4.263640e-06  1.701292e-06
## Naloxone_Pharmacy_Yes_Redefined                -9.693092e-06 -4.335218e-06
## Naloxone_Pharmacy_No_Redefined                 -5.773398e-06 -1.607156e-06
## Medical_Marijuana_Redefined                     6.354468e-06  1.094530e-05
## Recreational_Marijuana_Redefined               -1.433592e-05 -8.742271e-06
## GSL_Redefined                                   2.180344e-06  6.150972e-06
## PDMP_Redefined                                 -1.905469e-05 -1.594534e-05
## Medicaid_Expansion_Redefined                    9.070130e-06  1.341748e-05
## neg_2_pd                                       -5.924682e-06 -4.443708e-07
## neg_3_pd                                       -5.431833e-06  2.553242e-07
## neg_4_pd                                       -9.092257e-06 -3.100244e-06
## neg_5_pd                                       -1.098886e-05 -5.532630e-06
## neg_6_pd                                       -1.113919e-05 -5.831373e-06
## neg_7_pd                                       -1.540913e-05 -9.094939e-06
## neg_8_pd                                       -1.975811e-05 -1.185350e-05
## neg_9_pd                                       -1.446516e-05 -8.192513e-06
## neg_10_pd                                      -1.411553e-05 -8.269582e-06
## neg_11_pd                                      -1.549125e-05 -9.349852e-06
## neg_12_pd                                      -1.316649e-05 -5.951537e-06
## neg_13_pd                                      -1.608167e-05 -9.391280e-06
## neg_14_pd                                      -1.850258e-05 -1.067322e-05
## neg_15_pd                                      -2.456176e-05 -1.487699e-05
## neg_16_pd                                      -2.188313e-05 -1.448732e-05
## neg_17_pd                                      -2.571926e-05 -1.772553e-05
## neg_18_pd                                      -2.691398e-05 -1.866777e-05
## neg_19_pd                                      -2.826921e-05 -1.931907e-05
## neg_20_pd                                      -3.074698e-05 -2.165852e-05
## neg_21_pd                                      -3.180203e-05 -2.101830e-05
## neg_22_pd                                      -3.489513e-05 -2.126153e-05
## neg_23_pd                                      -3.177972e-05 -1.874855e-05
## neg_24_pd                                      -3.810040e-05 -2.300221e-05
## neg_25_pd                                      -3.725609e-05 -2.052759e-05
## neg_26_pd                                      -3.552791e-05 -1.630307e-05
## neg_27_pd                                      -2.917577e-05 -1.568866e-05
## neg_28_pd                                      -2.739710e-05 -1.507752e-05
## neg_29_pd                                      -2.244514e-05 -1.224774e-05
## neg_30_pd                                      -2.827549e-05 -1.690021e-05
## neg_31_pd                                      -3.134989e-05 -1.852997e-05
## neg_32_pd                                      -3.298367e-05 -1.877590e-05
## neg_33_pd                                      -3.024011e-05 -1.240748e-05
## pos_0_pd                                       -5.579131e-06  2.539847e-08
## pos_1_pd                                       -7.658457e-06 -1.352591e-06
## pos_2_pd                                       -4.646623e-06  1.644575e-06
## pos_3_pd                                       -6.634944e-06 -9.336550e-09
## pos_4_pd                                       -6.358173e-06  5.732680e-07
## pos_5_pd                                       -8.633026e-06 -1.837598e-06
## pos_6_pd                                       -7.744238e-06  2.345472e-07
## pos_7_pd                                       -8.281404e-06 -5.369095e-07
## pos_8_pd                                       -1.054788e-05 -1.868906e-06
## pos_9_pd                                       -1.046480e-05 -3.140505e-06
## pos_10_pd                                      -1.085704e-05 -3.393235e-06
## pos_11_pd                                      -1.060797e-05 -3.053075e-06
## pos_12_pd                                      -9.146633e-06 -1.999758e-06
## pos_13_pd                                      -1.372242e-05 -5.156054e-06
## pos_14_pd                                      -1.174593e-05 -3.669463e-06
## pos_15_pd                                      -1.336103e-05 -5.162032e-06
## pos_16_pd                                      -1.480096e-05 -6.156197e-06
## pos_17_pd                                      -1.268278e-05 -4.155646e-06
## pos_18_pd                                      -1.200255e-05 -3.494411e-06
## pos_19_pd                                      -1.098053e-05 -2.674879e-06
## pos_20_pd                                      -1.269841e-05 -3.948372e-06
## pos_21_pd                                      -1.364231e-05 -4.240683e-06
## pos_22_pd                                      -1.157539e-05 -1.785388e-06
## pos_23_pd                                      -1.213957e-05 -8.797009e-07
## pos_24_pd                                      -1.532456e-05 -4.155083e-06
## pos_25_pd                                      -1.378720e-05 -1.944884e-06
## pos_26_pd                                      -1.331314e-05 -1.574143e-06
## pos_27_pd                                      -1.533870e-05 -4.657655e-06
## pos_28_pd                                      -1.329562e-05 -1.813360e-06
## pos_29_pd                                      -1.727459e-05 -5.020296e-06
## pos_30_pd                                      -1.221141e-05  4.239406e-07
## pos_31_pd                                      -4.662830e-06  1.237751e-05
## pos_32_pd                                      -1.280091e-05  1.022893e-05
## pos_33_pd                                      -1.693527e-05  9.606784e-06
## pos_34_pd                                      -1.845457e-05  1.713385e-05
## pos_35_pd                                      -2.677365e-05  2.666542e-06
## pos_36_pd                                      -2.342568e-05 -1.435736e-06
## pos_37_pd                                      -1.467661e-05  1.587176e-05
## pos_38_pd                                      -3.296841e-05  1.613912e-05
## pos_39_pd                                      -4.235862e-05  2.397159e-05
## s(Time_Period_ID):as.factor(Region)Midwest.1   -2.640022e-05 -1.864013e-05
## s(Time_Period_ID):as.factor(Region)Midwest.2   -2.013501e-05 -1.437385e-05
## s(Time_Period_ID):as.factor(Region)Midwest.3   -8.399754e-06 -3.599267e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4   -3.158193e-07  4.625205e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5    7.163758e-06  1.142176e-05
## s(Time_Period_ID):as.factor(Region)Midwest.6    1.351382e-05  1.852194e-05
## s(Time_Period_ID):as.factor(Region)Midwest.7    2.268163e-05  2.938898e-05
## s(Time_Period_ID):as.factor(Region)Midwest.8    3.758518e-05  4.786244e-05
## s(Time_Period_ID):as.factor(Region)Midwest.9    2.922265e-05  4.221937e-05
## s(Time_Period_ID):as.factor(Region)Northeast.1 -3.376645e-05 -2.571216e-05
## s(Time_Period_ID):as.factor(Region)Northeast.2 -2.715192e-05 -2.068205e-05
## s(Time_Period_ID):as.factor(Region)Northeast.3 -7.775770e-06 -1.776697e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 -1.017321e-05 -4.355934e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 -9.497047e-06 -2.830569e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6  1.544824e-06  8.662558e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7  3.467209e-05  4.494980e-05
## s(Time_Period_ID):as.factor(Region)Northeast.8  7.938016e-05  9.100157e-05
## s(Time_Period_ID):as.factor(Region)Northeast.9  5.934945e-05  7.443454e-05
## s(Time_Period_ID):as.factor(Region)South.1     -2.824074e-05 -2.113765e-05
## s(Time_Period_ID):as.factor(Region)South.2     -1.601769e-05 -1.120885e-05
## s(Time_Period_ID):as.factor(Region)South.3     -1.728669e-06  3.964908e-06
## s(Time_Period_ID):as.factor(Region)South.4      4.351275e-06  1.007624e-05
## s(Time_Period_ID):as.factor(Region)South.5      1.354175e-05  1.860495e-05
## s(Time_Period_ID):as.factor(Region)South.6      1.637320e-05  2.195783e-05
## s(Time_Period_ID):as.factor(Region)South.7      2.859844e-05  3.560566e-05
## s(Time_Period_ID):as.factor(Region)South.8      5.024253e-05  6.216590e-05
## s(Time_Period_ID):as.factor(Region)South.9      3.351791e-05  5.259294e-05
## s(Time_Period_ID):as.factor(Region)West.1      -1.614422e-05 -1.176282e-05
## s(Time_Period_ID):as.factor(Region)West.2      -9.293793e-06 -5.525065e-06
## s(Time_Period_ID):as.factor(Region)West.3      -2.002912e-06  2.332601e-06
## s(Time_Period_ID):as.factor(Region)West.4       4.947686e-06  8.801392e-06
## s(Time_Period_ID):as.factor(Region)West.5       9.085742e-06  1.335974e-05
## s(Time_Period_ID):as.factor(Region)West.6       1.156459e-05  1.671415e-05
## s(Time_Period_ID):as.factor(Region)West.7       1.362680e-05  1.974457e-05
## s(Time_Period_ID):as.factor(Region)West.8       1.814801e-05  2.576047e-05
## s(Time_Period_ID):as.factor(Region)West.9       1.753132e-05  2.670057e-05
##                                                      ub_coef      sd_coef
## (Intercept)                                     8.157547e-05 2.905074e-06
## StateAlaska                                     2.061533e-05 4.569480e-06
## StateArizona                                    2.395014e-05 3.163264e-06
## StateArkansas                                  -1.775207e-05 3.501809e-06
## StateCalifornia                                -1.172615e-05 3.695578e-06
## StateColorado                                   6.929043e-06 3.648614e-06
## StateConnecticut                                2.159818e-05 3.213467e-06
## StateDelaware                                   4.299841e-05 6.698533e-06
## StateFlorida                                    1.793385e-05 3.341016e-06
## StateGeorgia                                   -5.179450e-06 3.685194e-06
## StateHawaii                                    -1.915262e-05 3.690917e-06
## StateIdaho                                      5.248369e-06 3.170146e-06
## StateIllinois                                   8.699235e-06 3.110417e-06
## StateIndiana                                    2.002344e-05 2.915259e-06
## StateIowa                                      -2.803673e-05 2.865495e-06
## StateKansas                                    -1.140168e-05 2.390691e-06
## StateKentucky                                   6.802175e-05 3.404381e-06
## StateLouisiana                                  2.480617e-05 2.991510e-06
## StateMaine                                      1.826863e-05 3.878679e-06
## StateMaryland                                  -4.747562e-05 3.869157e-06
## StateMassachusetts                              2.860456e-05 3.503142e-06
## StateMichigan                                   8.021994e-06 2.619192e-06
## StateMinnesota                                 -3.153424e-05 3.359916e-06
## StateMississippi                                6.744176e-06 4.111735e-06
## StateMissouri                                   1.271329e-05 3.124578e-06
## StateMontana                                   -2.698445e-05 3.096056e-06
## StateNebraska                                  -2.816591e-05 3.151727e-06
## StateNevada                                     3.663927e-05 3.249801e-06
## StateNew Hampshire                              2.594134e-05 3.863192e-06
## StateNew Jersey                                 1.054923e-05 3.622777e-06
## StateNew Mexico                                 5.863983e-05 3.773061e-06
## StateNew York                                   5.733091e-07 4.565213e-06
## StateNorth Carolina                             1.548835e-05 2.353085e-06
## StateNorth Dakota                              -3.108441e-05 4.008816e-06
## StateOhio                                       5.238755e-05 7.188194e-06
## StateOklahoma                                   4.259911e-05 3.868445e-06
## StateOregon                                    -1.591605e-05 3.335425e-06
## StatePennsylvania                               4.855745e-05 3.478101e-06
## StateRhode Island                               3.419899e-05 4.483319e-06
## StateSouth Carolina                             2.464642e-05 3.179550e-06
## StateSouth Dakota                              -2.678978e-05 3.570635e-06
## StateTennessee                                  4.092187e-05 3.175156e-06
## StateTexas                                     -1.314586e-07 4.121663e-06
## StateUtah                                       1.103432e-05 4.137463e-06
## StateVermont                                   -3.100380e-06 4.428681e-06
## StateVirginia                                  -5.841921e-07 2.660677e-06
## StateWashington                                 1.359632e-06 3.573279e-06
## StateWest Virginia                              1.106453e-04 8.490531e-06
## StateWisconsin                                  2.008559e-06 2.987183e-06
## StateWyoming                                    7.666225e-06 3.043333e-06
## Naloxone_Pharmacy_Yes_Redefined                 1.022656e-06 2.733609e-06
## Naloxone_Pharmacy_No_Redefined                  2.559086e-06 2.125634e-06
## Medical_Marijuana_Redefined                     1.553614e-05 2.342262e-06
## Recreational_Marijuana_Redefined               -3.148625e-06 2.853901e-06
## GSL_Redefined                                   1.012160e-05 2.025831e-06
## PDMP_Redefined                                 -1.283599e-05 1.586404e-06
## Medicaid_Expansion_Redefined                    1.776483e-05 2.218035e-06
## neg_2_pd                                        5.035940e-06 2.796077e-06
## neg_3_pd                                        5.942481e-06 2.901611e-06
## neg_4_pd                                        2.891770e-06 3.057150e-06
## neg_5_pd                                       -7.639754e-08 2.783792e-06
## neg_6_pd                                       -5.235552e-07 2.708070e-06
## neg_7_pd                                       -2.780750e-06 3.221525e-06
## neg_8_pd                                       -3.948893e-06 4.032964e-06
## neg_9_pd                                       -1.919866e-06 3.200330e-06
## neg_10_pd                                      -2.423635e-06 2.982626e-06
## neg_11_pd                                      -3.208452e-06 3.133367e-06
## neg_12_pd                                       1.263419e-06 3.681100e-06
## neg_13_pd                                      -2.700889e-06 3.413465e-06
## neg_14_pd                                      -2.843863e-06 3.994572e-06
## neg_15_pd                                      -5.192220e-06 4.941209e-06
## neg_16_pd                                      -7.091510e-06 3.773374e-06
## neg_17_pd                                      -9.731808e-06 4.078431e-06
## neg_18_pd                                      -1.042156e-05 4.207250e-06
## neg_19_pd                                      -1.036893e-05 4.566398e-06
## neg_20_pd                                      -1.257006e-05 4.636969e-06
## neg_21_pd                                      -1.023457e-05 5.501905e-06
## neg_22_pd                                      -7.627931e-06 6.955918e-06
## neg_23_pd                                      -5.717382e-06 6.648554e-06
## neg_24_pd                                      -7.904028e-06 7.703156e-06
## neg_25_pd                                      -3.799090e-06 8.534948e-06
## neg_26_pd                                       2.921762e-06 9.808588e-06
## neg_27_pd                                      -2.201551e-06 6.881178e-06
## neg_28_pd                                      -2.757938e-06 6.285502e-06
## neg_29_pd                                      -2.050340e-06 5.202754e-06
## neg_30_pd                                      -5.524931e-06 5.803714e-06
## neg_31_pd                                      -5.710045e-06 6.540777e-06
## neg_32_pd                                      -4.568121e-06 7.248864e-06
## neg_33_pd                                       5.425142e-06 9.098279e-06
## pos_0_pd                                        5.629928e-06 2.859454e-06
## pos_1_pd                                        4.953275e-06 3.217279e-06
## pos_2_pd                                        7.935773e-06 3.209795e-06
## pos_3_pd                                        6.616271e-06 3.380412e-06
## pos_4_pd                                        7.504709e-06 3.536449e-06
## pos_5_pd                                        4.957829e-06 3.467055e-06
## pos_6_pd                                        8.213333e-06 4.070809e-06
## pos_7_pd                                        7.207585e-06 3.951273e-06
## pos_8_pd                                        6.810069e-06 4.428049e-06
## pos_9_pd                                        4.183794e-06 3.736887e-06
## pos_10_pd                                       4.070569e-06 3.808063e-06
## pos_11_pd                                       4.501821e-06 3.854539e-06
## pos_12_pd                                       5.147116e-06 3.646364e-06
## pos_13_pd                                       3.410312e-06 4.370594e-06
## pos_14_pd                                       4.407001e-06 4.120645e-06
## pos_15_pd                                       3.036962e-06 4.183160e-06
## pos_16_pd                                       2.488569e-06 4.410595e-06
## pos_17_pd                                       4.371486e-06 4.350578e-06
## pos_18_pd                                       5.013729e-06 4.340888e-06
## pos_19_pd                                       5.630775e-06 4.237579e-06
## pos_20_pd                                       4.801667e-06 4.464306e-06
## pos_21_pd                                       5.160940e-06 4.796747e-06
## pos_22_pd                                       8.004615e-06 4.994900e-06
## pos_23_pd                                       1.038017e-05 5.744830e-06
## pos_24_pd                                       7.014395e-06 5.698713e-06
## pos_25_pd                                       9.897435e-06 6.042000e-06
## pos_26_pd                                       1.016486e-05 5.989286e-06
## pos_27_pd                                       6.023389e-06 5.449512e-06
## pos_28_pd                                       9.668904e-06 5.858298e-06
## pos_29_pd                                       7.234001e-06 6.252192e-06
## pos_30_pd                                       1.305929e-05 6.446608e-06
## pos_31_pd                                       2.941786e-05 8.694053e-06
## pos_32_pd                                       3.325876e-05 1.174992e-05
## pos_33_pd                                       3.614884e-05 1.354187e-05
## pos_34_pd                                       5.272227e-05 1.815736e-05
## pos_35_pd                                       3.210673e-05 1.502051e-05
## pos_36_pd                                       2.055421e-05 1.121936e-05
## pos_37_pd                                       4.642012e-05 1.558590e-05
## pos_38_pd                                       6.524665e-05 2.505486e-05
## pos_39_pd                                       9.030181e-05 3.384195e-05
## s(Time_Period_ID):as.factor(Region)Midwest.1   -1.088004e-05 3.959229e-06
## s(Time_Period_ID):as.factor(Region)Midwest.2   -8.612697e-06 2.939365e-06
## s(Time_Period_ID):as.factor(Region)Midwest.3    1.201220e-06 2.449228e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4    9.566229e-06 2.520931e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5    1.567976e-05 2.172448e-06
## s(Time_Period_ID):as.factor(Region)Midwest.6    2.353006e-05 2.555163e-06
## s(Time_Period_ID):as.factor(Region)Midwest.7    3.609632e-05 3.422115e-06
## s(Time_Period_ID):as.factor(Region)Midwest.8    5.813971e-05 5.243501e-06
## s(Time_Period_ID):as.factor(Region)Midwest.9    5.521609e-05 6.630980e-06
## s(Time_Period_ID):as.factor(Region)Northeast.1 -1.765787e-05 4.109333e-06
## s(Time_Period_ID):as.factor(Region)Northeast.2 -1.421218e-05 3.300954e-06
## s(Time_Period_ID):as.factor(Region)Northeast.3  4.222376e-06 3.060752e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4  1.461345e-06 2.968000e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5  3.835908e-06 3.401264e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6  1.578029e-05 3.631497e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7  5.522750e-05 5.243728e-06
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.026230e-04 5.929289e-06
## s(Time_Period_ID):as.factor(Region)Northeast.9  8.951963e-05 7.696475e-06
## s(Time_Period_ID):as.factor(Region)South.1     -1.403456e-05 3.624025e-06
## s(Time_Period_ID):as.factor(Region)South.2     -6.400009e-06 2.453490e-06
## s(Time_Period_ID):as.factor(Region)South.3      9.658485e-06 2.904886e-06
## s(Time_Period_ID):as.factor(Region)South.4      1.580121e-05 2.920901e-06
## s(Time_Period_ID):as.factor(Region)South.5      2.366816e-05 2.583268e-06
## s(Time_Period_ID):as.factor(Region)South.6      2.754245e-05 2.849298e-06
## s(Time_Period_ID):as.factor(Region)South.7      4.261288e-05 3.575113e-06
## s(Time_Period_ID):as.factor(Region)South.8      7.408928e-05 6.083354e-06
## s(Time_Period_ID):as.factor(Region)South.9      7.166797e-05 9.732157e-06
## s(Time_Period_ID):as.factor(Region)West.1      -7.381414e-06 2.235410e-06
## s(Time_Period_ID):as.factor(Region)West.2      -1.756337e-06 1.922820e-06
## s(Time_Period_ID):as.factor(Region)West.3       6.668115e-06 2.211997e-06
## s(Time_Period_ID):as.factor(Region)West.4       1.265510e-05 1.966176e-06
## s(Time_Period_ID):as.factor(Region)West.5       1.763374e-05 2.180611e-06
## s(Time_Period_ID):as.factor(Region)West.6       2.186371e-05 2.627328e-06
## s(Time_Period_ID):as.factor(Region)West.7       2.586233e-05 3.121310e-06
## s(Time_Period_ID):as.factor(Region)West.8       3.337294e-05 3.883911e-06
## s(Time_Period_ID):as.factor(Region)West.9       3.586982e-05 4.678189e-06
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")

5.2.3 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study <- sensitivity_anlys_event_study_sd_and_ci %>%
  mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

5.3 Analysis With Only Periods After Treatment

formula_post_tx <- formula(paste("prop_dead~ State +
                                           s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model<-gam(formula_post_tx,
                                         data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## prop_dead ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + pos_5_pd + 
##     pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + pos_11_pd + 
##     pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + pos_16_pd + 
##     pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + pos_21_pd + 
##     pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + pos_26_pd + 
##     pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd + pos_31_pd + 
##     pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd + pos_36_pd + 
##     pos_37_pd + pos_38_pd + pos_39_pd
## 
## Parametric coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       7.615e-05  3.494e-06  21.792  < 2e-16 ***
## StateAlaska                      -1.244e-07  4.815e-06  -0.026 0.979395    
## StateArizona                      1.048e-05  4.332e-06   2.419 0.015668 *  
## StateArkansas                    -2.994e-05  4.258e-06  -7.032 2.84e-12 ***
## StateCalifornia                  -1.081e-05  4.866e-06  -2.222 0.026413 *  
## StateColorado                    -6.902e-06  4.740e-06  -1.456 0.145555    
## StateConnecticut                  1.527e-05  4.502e-06   3.393 0.000707 ***
## StateDelaware                     1.855e-05  4.405e-06   4.211 2.67e-05 ***
## StateFlorida                      2.123e-05  4.454e-06   4.767 2.01e-06 ***
## StateGeorgia                     -1.127e-06  4.557e-06  -0.247 0.804631    
## StateHawaii                      -2.801e-05  4.732e-06  -5.919 3.85e-09 ***
## StateIdaho                       -1.165e-05  4.300e-06  -2.709 0.006816 ** 
## StateIllinois                     1.011e-05  4.410e-06   2.292 0.022016 *  
## StateIndiana                      1.100e-05  4.214e-06   2.610 0.009117 ** 
## StateIowa                        -2.866e-05  4.271e-06  -6.712 2.53e-11 ***
## StateKansas                      -1.528e-05  4.188e-06  -3.648 0.000272 ***
## StateKentucky                     5.570e-05  4.257e-06  13.084  < 2e-16 ***
## StateLouisiana                    2.460e-05  4.242e-06   5.799 7.82e-09 ***
## StateMaine                        7.917e-06  4.699e-06   1.685 0.092192 .  
## StateMaryland                    -4.704e-05  4.408e-06 -10.670  < 2e-16 ***
## StateMassachusetts                2.122e-05  4.267e-06   4.973 7.21e-07 ***
## StateMichigan                     5.732e-06  4.363e-06   1.314 0.189042    
## StateMinnesota                   -3.764e-05  4.434e-06  -8.487  < 2e-16 ***
## StateMississippi                 -1.064e-05  4.248e-06  -2.505 0.012340 *  
## StateMissouri                     1.052e-05  4.346e-06   2.420 0.015612 *  
## StateMontana                     -2.781e-05  4.518e-06  -6.154 9.20e-10 ***
## StateNebraska                    -4.189e-05  4.300e-06  -9.743  < 2e-16 ***
## StateNevada                       3.271e-05  4.577e-06   7.147 1.26e-12 ***
## StateNew Hampshire                1.527e-05  4.269e-06   3.578 0.000356 ***
## StateNew Jersey                   1.124e-05  4.418e-06   2.544 0.011053 *  
## StateNew Mexico                   4.761e-05  4.644e-06  10.252  < 2e-16 ***
## StateNew York                    -7.913e-06  4.336e-06  -1.825 0.068146 .  
## StateNorth Carolina               1.502e-05  4.204e-06   3.573 0.000362 ***
## StateNorth Dakota                -4.662e-05  4.257e-06 -10.950  < 2e-16 ***
## StateOhio                         4.935e-05  4.575e-06  10.786  < 2e-16 ***
## StateOklahoma                     2.980e-05  4.230e-06   7.046 2.58e-12 ***
## StateOregon                      -2.570e-05  4.701e-06  -5.467 5.18e-08 ***
## StatePennsylvania                 5.130e-05  4.467e-06  11.486  < 2e-16 ***
## StateRhode Island                 1.597e-05  4.457e-06   3.582 0.000349 ***
## StateSouth Carolina               7.442e-06  4.287e-06   1.736 0.082689 .  
## StateSouth Dakota                -4.505e-05  4.326e-06 -10.413  < 2e-16 ***
## StateTennessee                    3.460e-05  4.160e-06   8.317  < 2e-16 ***
## StateTexas                        6.825e-07  4.430e-06   0.154 0.877569    
## StateUtah                         6.117e-06  4.212e-06   1.452 0.146556    
## StateVermont                     -1.471e-05  4.429e-06  -3.321 0.000915 ***
## StateVirginia                     4.207e-07  4.265e-06   0.099 0.921428    
## StateWashington                  -7.392e-06  4.780e-06  -1.546 0.122161    
## StateWest Virginia                8.612e-05  4.273e-06  20.157  < 2e-16 ***
## StateWisconsin                    1.870e-06  4.251e-06   0.440 0.659998    
## StateWyoming                     -8.478e-07  4.190e-06  -0.202 0.839667    
## Naloxone_Pharmacy_Yes_Redefined  -4.107e-06  2.766e-06  -1.485 0.137742    
## Naloxone_Pharmacy_No_Redefined   -1.422e-06  2.470e-06  -0.576 0.564837    
## Medical_Marijuana_Redefined       1.175e-05  1.971e-06   5.962 2.96e-09 ***
## Recreational_Marijuana_Redefined -7.271e-06  3.118e-06  -2.332 0.019825 *  
## GSL_Redefined                     5.841e-06  2.019e-06   2.894 0.003853 ** 
## PDMP_Redefined                   -1.517e-05  1.577e-06  -9.625  < 2e-16 ***
## Medicaid_Expansion_Redefined      1.283e-05  1.946e-06   6.590 5.69e-11 ***
## pos_0_pd                          1.590e-06  2.918e-06   0.545 0.585919    
## pos_1_pd                         -4.270e-07  2.952e-06  -0.145 0.885022    
## pos_2_pd                          1.953e-06  2.987e-06   0.654 0.513330    
## pos_3_pd                         -3.404e-07  3.025e-06  -0.113 0.910420    
## pos_4_pd                         -4.024e-07  3.065e-06  -0.131 0.895557    
## pos_5_pd                         -3.434e-06  3.114e-06  -1.103 0.270378    
## pos_6_pd                         -1.994e-06  3.173e-06  -0.628 0.529849    
## pos_7_pd                         -3.450e-06  3.228e-06  -1.069 0.285376    
## pos_8_pd                         -5.473e-06  3.320e-06  -1.648 0.099438 .  
## pos_9_pd                         -7.470e-06  3.394e-06  -2.201 0.027873 *  
## pos_10_pd                        -8.429e-06  3.442e-06  -2.449 0.014421 *  
## pos_11_pd                        -8.824e-06  3.518e-06  -2.508 0.012218 *  
## pos_12_pd                        -8.503e-06  3.596e-06  -2.365 0.018153 *  
## pos_13_pd                        -1.234e-05  3.651e-06  -3.380 0.000740 ***
## pos_14_pd                        -1.159e-05  3.785e-06  -3.062 0.002229 ** 
## pos_15_pd                        -1.383e-05  3.878e-06  -3.567 0.000371 ***
## pos_16_pd                        -1.553e-05  3.945e-06  -3.937 8.55e-05 ***
## pos_17_pd                        -1.427e-05  4.093e-06  -3.487 0.000499 ***
## pos_18_pd                        -1.435e-05  4.194e-06  -3.422 0.000635 ***
## pos_19_pd                        -1.417e-05  4.259e-06  -3.327 0.000896 ***
## pos_20_pd                        -1.620e-05  4.441e-06  -3.648 0.000271 ***
## pos_21_pd                        -1.719e-05  4.627e-06  -3.716 0.000208 ***
## pos_22_pd                        -1.544e-05  4.740e-06  -3.257 0.001145 ** 
## pos_23_pd                        -1.527e-05  4.877e-06  -3.130 0.001773 ** 
## pos_24_pd                        -1.916e-05  5.183e-06  -3.697 0.000225 ***
## pos_25_pd                        -1.759e-05  5.476e-06  -3.212 0.001338 ** 
## pos_26_pd                        -1.791e-05  5.535e-06  -3.236 0.001234 ** 
## pos_27_pd                        -2.179e-05  5.610e-06  -3.883 0.000107 ***
## pos_28_pd                        -1.954e-05  5.697e-06  -3.430 0.000617 ***
## pos_29_pd                        -2.341e-05  6.195e-06  -3.779 0.000162 ***
## pos_30_pd                        -1.866e-05  6.400e-06  -2.916 0.003586 ** 
## pos_31_pd                        -7.543e-06  6.621e-06  -1.139 0.254670    
## pos_32_pd                        -1.054e-05  7.294e-06  -1.445 0.148697    
## pos_33_pd                        -1.192e-05  7.629e-06  -1.562 0.118365    
## pos_34_pd                        -5.050e-06  7.709e-06  -0.655 0.512508    
## pos_35_pd                        -2.019e-05  8.956e-06  -2.254 0.024301 *  
## pos_36_pd                        -2.494e-05  9.045e-06  -2.758 0.005875 ** 
## pos_37_pd                        -8.400e-06  1.070e-05  -0.785 0.432654    
## pos_38_pd                        -8.735e-06  1.429e-05  -0.611 0.541172    
## pos_39_pd                        -1.579e-06  1.446e-05  -0.109 0.913036    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df     F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   6.822  7.911 49.06  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.047  8.756 79.14  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     7.779  8.613 73.93  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      3.300  4.122 62.06  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.835   Deviance explained = 84.5%
## GCV = 3.6751e-10  Scale est. = 3.4492e-10  n = 2000

5.3.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx <- data.frame(predict(sensitivity_anlys_post_tx_model, type = "lpmatrix"))

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx <- coef(sensitivity_anlys_post_tx_model)

sensitivity_anlys_post_tx_sd_and_ci <- compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_post_tx), 
                                                         sensitivity_anlys_event_study_data$prop_dead,
                                                         coefficient_values_sensitivity_anlys_post_tx,
                                                         p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx) - 50)
sensitivity_anlys_post_tx_sd_and_ci
##                                                      lb_coef   coef_values
## (Intercept)                                     7.139855e-05  7.615063e-05
## StateAlaska                                    -8.051122e-06 -1.243671e-07
## StateArizona                                    4.830838e-06  1.047917e-05
## StateArkansas                                  -3.660598e-05 -2.994465e-05
## StateCalifornia                                -1.778510e-05 -1.081069e-05
## StateColorado                                  -1.359417e-05 -6.902221e-06
## StateConnecticut                                9.002599e-06  1.527196e-05
## StateDelaware                                   6.704041e-06  1.854851e-05
## StateFlorida                                    1.543359e-05  2.123426e-05
## StateGeorgia                                   -7.525247e-06 -1.127323e-06
## StateHawaii                                    -3.507774e-05 -2.800827e-05
## StateIdaho                                     -1.651843e-05 -1.164810e-05
## StateIllinois                                   4.319206e-06  1.010830e-05
## StateIndiana                                    5.286176e-06  1.099931e-05
## StateIowa                                      -3.385601e-05 -2.866399e-05
## StateKansas                                    -1.986427e-05 -1.527660e-05
## StateKentucky                                   4.906042e-05  5.569746e-05
## StateLouisiana                                  1.912834e-05  2.459979e-05
## StateMaine                                      4.714770e-07  7.917008e-06
## StateMaryland                                  -5.429863e-05 -4.703545e-05
## StateMassachusetts                              1.436466e-05  2.121827e-05
## StateMichigan                                   6.996377e-07  5.732447e-06
## StateMinnesota                                 -4.409755e-05 -3.763627e-05
## StateMississippi                               -1.787561e-05 -1.063882e-05
## StateMissouri                                   4.692188e-06  1.051648e-05
## StateMontana                                   -3.355921e-05 -2.780680e-05
## StateNebraska                                  -4.762309e-05 -4.188786e-05
## StateNevada                                     2.640169e-05  3.271259e-05
## StateNew Hampshire                              7.772563e-06  1.527174e-05
## StateNew Jersey                                 4.575249e-06  1.123726e-05
## StateNew Mexico                                 4.036531e-05  4.761186e-05
## StateNew York                                  -1.675067e-05 -7.913039e-06
## StateNorth Carolina                             1.067636e-05  1.501899e-05
## StateNorth Dakota                              -5.398294e-05 -4.661541e-05
## StateOhio                                       3.566787e-05  4.935159e-05
## StateOklahoma                                   2.243402e-05  2.980233e-05
## StateOregon                                    -3.202076e-05 -2.570197e-05
## StatePennsylvania                               4.492220e-05  5.130490e-05
## StateRhode Island                               7.594812e-06  1.596700e-05
## StateSouth Carolina                             2.721784e-06  7.442319e-06
## StateSouth Dakota                              -5.143228e-05 -4.504805e-05
## StateTennessee                                  2.848882e-05  3.459578e-05
## StateTexas                                     -7.215531e-06  6.825124e-07
## StateUtah                                      -2.039631e-06  6.116769e-06
## StateVermont                                   -2.327214e-05 -1.470731e-05
## StateVirginia                                  -4.587674e-06  4.206861e-07
## StateWashington                                -1.429859e-05 -7.391705e-06
## StateWest Virginia                              6.951595e-05  8.612320e-05
## StateWisconsin                                 -3.533923e-06  1.870202e-06
## StateWyoming                                   -6.889956e-06 -8.478496e-07
## Naloxone_Pharmacy_Yes_Redefined                -9.432775e-06 -4.107253e-06
## Naloxone_Pharmacy_No_Redefined                 -5.568562e-06 -1.422226e-06
## Medical_Marijuana_Redefined                     7.199413e-06  1.175190e-05
## Recreational_Marijuana_Redefined               -1.262468e-05 -7.270518e-06
## GSL_Redefined                                   1.904319e-06  5.840877e-06
## PDMP_Redefined                                 -1.822667e-05 -1.517500e-05
## Medicaid_Expansion_Redefined                    8.537038e-06  1.282744e-05
## pos_0_pd                                       -2.965098e-06  1.589816e-06
## pos_1_pd                                       -5.840947e-06 -4.269689e-07
## pos_2_pd                                       -3.408478e-06  1.952849e-06
## pos_3_pd                                       -6.011940e-06 -3.403996e-07
## pos_4_pd                                       -6.289188e-06 -4.023682e-07
## pos_5_pd                                       -9.197525e-06 -3.433682e-06
## pos_6_pd                                       -8.932879e-06 -1.993884e-06
## pos_7_pd                                       -1.022580e-05 -3.449720e-06
## pos_8_pd                                       -1.313667e-05 -5.473039e-06
## pos_9_pd                                       -1.385605e-05 -7.469612e-06
## pos_10_pd                                      -1.500229e-05 -8.429489e-06
## pos_11_pd                                      -1.540069e-05 -8.823831e-06
## pos_12_pd                                      -1.471607e-05 -8.502757e-06
## pos_13_pd                                      -1.999956e-05 -1.233928e-05
## pos_14_pd                                      -1.858506e-05 -1.158885e-05
## pos_15_pd                                      -2.092374e-05 -1.383004e-05
## pos_16_pd                                      -2.312394e-05 -1.553093e-05
## pos_17_pd                                      -2.177377e-05 -1.427438e-05
## pos_18_pd                                      -2.158529e-05 -1.435308e-05
## pos_19_pd                                      -2.127088e-05 -1.416703e-05
## pos_20_pd                                      -2.355906e-05 -1.620249e-05
## pos_21_pd                                      -2.521230e-05 -1.719404e-05
## pos_22_pd                                      -2.388111e-05 -1.544116e-05
## pos_23_pd                                      -2.529719e-05 -1.526768e-05
## pos_24_pd                                      -2.909569e-05 -1.916142e-05
## pos_25_pd                                      -2.826441e-05 -1.759028e-05
## pos_26_pd                                      -2.860727e-05 -1.791097e-05
## pos_27_pd                                      -3.099788e-05 -2.178720e-05
## pos_28_pd                                      -2.973838e-05 -1.953942e-05
## pos_29_pd                                      -3.442329e-05 -2.341014e-05
## pos_30_pd                                      -3.009266e-05 -1.866474e-05
## pos_31_pd                                      -2.356847e-05 -7.543544e-06
## pos_32_pd                                      -3.271810e-05 -1.053846e-05
## pos_33_pd                                      -3.773946e-05 -1.191918e-05
## pos_34_pd                                      -4.012237e-05 -5.049810e-06
## pos_35_pd                                      -4.883116e-05 -2.018769e-05
## pos_36_pd                                      -4.583816e-05 -2.494403e-05
## pos_37_pd                                      -3.797048e-05 -8.400120e-06
## pos_38_pd                                      -5.707690e-05 -8.735278e-06
## pos_39_pd                                      -6.713461e-05 -1.579383e-06
## s(Time_Period_ID):as.factor(Region)Midwest.1   -3.211010e-05 -2.493444e-05
## s(Time_Period_ID):as.factor(Region)Midwest.2   -2.371188e-05 -1.830146e-05
## s(Time_Period_ID):as.factor(Region)Midwest.3   -9.157463e-06 -4.474457e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4    1.423613e-06  6.323655e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5    1.213292e-05  1.641477e-05
## s(Time_Period_ID):as.factor(Region)Midwest.6    2.158643e-05  2.650577e-05
## s(Time_Period_ID):as.factor(Region)Midwest.7    3.422336e-05  4.037425e-05
## s(Time_Period_ID):as.factor(Region)Midwest.8    5.252596e-05  6.239041e-05
## s(Time_Period_ID):as.factor(Region)Midwest.9    4.466238e-05  5.730285e-05
## s(Time_Period_ID):as.factor(Region)Northeast.1 -3.872057e-05 -3.093339e-05
## s(Time_Period_ID):as.factor(Region)Northeast.2 -3.149449e-05 -2.507869e-05
## s(Time_Period_ID):as.factor(Region)Northeast.3 -7.592004e-06 -1.599376e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4 -6.658618e-06 -1.012325e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5 -3.754892e-06  2.525880e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6  1.069200e-05  1.736867e-05
## s(Time_Period_ID):as.factor(Region)Northeast.7  4.670155e-05  5.626171e-05
## s(Time_Period_ID):as.factor(Region)Northeast.8  9.516824e-05  1.060037e-04
## s(Time_Period_ID):as.factor(Region)Northeast.9  7.494540e-05  8.947043e-05
## s(Time_Period_ID):as.factor(Region)South.1     -3.385393e-05 -2.733642e-05
## s(Time_Period_ID):as.factor(Region)South.2     -2.045537e-05 -1.584398e-05
## s(Time_Period_ID):as.factor(Region)South.3     -3.048268e-06  2.516412e-06
## s(Time_Period_ID):as.factor(Region)South.4      6.282816e-06  1.198599e-05
## s(Time_Period_ID):as.factor(Region)South.5      1.908371e-05  2.394614e-05
## s(Time_Period_ID):as.factor(Region)South.6      2.476099e-05  2.985264e-05
## s(Time_Period_ID):as.factor(Region)South.7      4.033239e-05  4.676438e-05
## s(Time_Period_ID):as.factor(Region)South.8      6.465526e-05  7.656179e-05
## s(Time_Period_ID):as.factor(Region)South.9      4.922028e-05  6.782284e-05
## s(Time_Period_ID):as.factor(Region)West.1      -2.196381e-05 -1.743681e-05
## s(Time_Period_ID):as.factor(Region)West.2      -1.269009e-05 -9.040207e-06
## s(Time_Period_ID):as.factor(Region)West.3      -2.486098e-06  1.767265e-06
## s(Time_Period_ID):as.factor(Region)West.4       7.415034e-06  1.114857e-05
## s(Time_Period_ID):as.factor(Region)West.5       1.461424e-05  1.850163e-05
## s(Time_Period_ID):as.factor(Region)West.6       1.993230e-05  2.454423e-05
## s(Time_Period_ID):as.factor(Region)West.7       2.454761e-05  3.005842e-05
## s(Time_Period_ID):as.factor(Region)West.8       3.212598e-05  3.927979e-05
## s(Time_Period_ID):as.factor(Region)West.9       3.218580e-05  4.072767e-05
##                                                      ub_coef      sd_coef
## (Intercept)                                     8.090271e-05 2.424530e-06
## StateAlaska                                     7.802388e-06 4.044263e-06
## StateArizona                                    1.612749e-05 2.881800e-06
## StateArkansas                                  -2.328331e-05 3.398640e-06
## StateCalifornia                                -3.836271e-06 3.558376e-06
## StateColorado                                  -2.102737e-07 3.414259e-06
## StateConnecticut                                2.154131e-05 3.198651e-06
## StateDelaware                                   3.039297e-05 6.043094e-06
## StateFlorida                                    2.703492e-05 2.959524e-06
## StateGeorgia                                    5.270602e-06 3.264247e-06
## StateHawaii                                    -2.093881e-05 3.606869e-06
## StateIdaho                                     -6.777775e-06 2.484862e-06
## StateIllinois                                   1.589740e-05 2.953622e-06
## StateIndiana                                    1.671244e-05 2.914864e-06
## StateIowa                                      -2.347198e-05 2.648987e-06
## StateKansas                                    -1.068894e-05 2.340648e-06
## StateKentucky                                   6.233450e-05 3.386243e-06
## StateLouisiana                                  3.007123e-05 2.791554e-06
## StateMaine                                      1.536254e-05 3.798740e-06
## StateMaryland                                  -3.977228e-05 3.705704e-06
## StateMassachusetts                              2.807187e-05 3.496738e-06
## StateMichigan                                   1.076526e-05 2.567760e-06
## StateMinnesota                                 -3.117500e-05 3.296567e-06
## StateMississippi                               -3.402037e-06 3.692238e-06
## StateMissouri                                   1.634077e-05 2.971578e-06
## StateMontana                                   -2.205439e-05 2.934903e-06
## StateNebraska                                  -3.615263e-05 2.926138e-06
## StateNevada                                     3.902349e-05 3.219848e-06
## StateNew Hampshire                              2.277091e-05 3.826109e-06
## StateNew Jersey                                 1.789928e-05 3.398987e-06
## StateNew Mexico                                 5.485840e-05 3.697216e-06
## StateNew York                                   9.245956e-07 4.508997e-06
## StateNorth Carolina                             1.936162e-05 2.215627e-06
## StateNorth Dakota                              -3.924788e-05 3.758944e-06
## StateOhio                                       6.303530e-05 6.981486e-06
## StateOklahoma                                   3.717064e-05 3.759342e-06
## StateOregon                                    -1.938317e-05 3.223875e-06
## StatePennsylvania                               5.768761e-05 3.256481e-06
## StateRhode Island                               2.433920e-05 4.271527e-06
## StateSouth Carolina                             1.216285e-05 2.408436e-06
## StateSouth Dakota                              -3.866382e-05 3.257261e-06
## StateTennessee                                  4.070274e-05 3.115794e-06
## StateTexas                                      8.580556e-06 4.029614e-06
## StateUtah                                       1.427317e-05 4.161429e-06
## StateVermont                                   -6.142477e-06 4.369811e-06
## StateVirginia                                   5.429046e-06 2.555286e-06
## StateWashington                                -4.848192e-07 3.523921e-06
## StateWest Virginia                              1.027305e-04 8.473088e-06
## StateWisconsin                                  7.274327e-06 2.757207e-06
## StateWyoming                                    5.194256e-06 3.082707e-06
## Naloxone_Pharmacy_Yes_Redefined                 1.218270e-06 2.717103e-06
## Naloxone_Pharmacy_No_Redefined                  2.724111e-06 2.115478e-06
## Medical_Marijuana_Redefined                     1.630438e-05 2.322695e-06
## Recreational_Marijuana_Redefined               -1.916352e-06 2.731717e-06
## GSL_Redefined                                   9.777435e-06 2.008448e-06
## PDMP_Redefined                                 -1.212333e-05 1.556976e-06
## Medicaid_Expansion_Redefined                    1.711783e-05 2.188979e-06
## pos_0_pd                                        6.144729e-06 2.323936e-06
## pos_1_pd                                        4.987009e-06 2.762233e-06
## pos_2_pd                                        7.314176e-06 2.735371e-06
## pos_3_pd                                        5.331141e-06 2.893643e-06
## pos_4_pd                                        5.484452e-06 3.003480e-06
## pos_5_pd                                        2.330162e-06 2.940736e-06
## pos_6_pd                                        4.945110e-06 3.540303e-06
## pos_7_pd                                        3.326362e-06 3.457185e-06
## pos_8_pd                                        2.190595e-06 3.910018e-06
## pos_9_pd                                       -1.083178e-06 3.258385e-06
## pos_10_pd                                      -1.856691e-06 3.353469e-06
## pos_11_pd                                      -2.246967e-06 3.355543e-06
## pos_12_pd                                      -2.289445e-06 3.170057e-06
## pos_13_pd                                      -4.678991e-06 3.908308e-06
## pos_14_pd                                      -4.592634e-06 3.569496e-06
## pos_15_pd                                      -6.736345e-06 3.619233e-06
## pos_16_pd                                      -7.937906e-06 3.873990e-06
## pos_17_pd                                      -6.774981e-06 3.826223e-06
## pos_18_pd                                      -7.120875e-06 3.689901e-06
## pos_19_pd                                      -7.063178e-06 3.624413e-06
## pos_20_pd                                      -8.845924e-06 3.753351e-06
## pos_21_pd                                      -9.175768e-06 4.090953e-06
## pos_22_pd                                      -7.001196e-06 4.306102e-06
## pos_23_pd                                      -5.238178e-06 5.117094e-06
## pos_24_pd                                      -9.227145e-06 5.068507e-06
## pos_25_pd                                      -6.916147e-06 5.445985e-06
## pos_26_pd                                      -7.214666e-06 5.457296e-06
## pos_27_pd                                      -1.257652e-05 4.699326e-06
## pos_28_pd                                      -9.340455e-06 5.203553e-06
## pos_29_pd                                      -1.239698e-05 5.618957e-06
## pos_30_pd                                      -7.236820e-06 5.830571e-06
## pos_31_pd                                       8.481383e-06 8.175983e-06
## pos_32_pd                                       1.164118e-05 1.131614e-05
## pos_33_pd                                       1.390111e-05 1.317361e-05
## pos_34_pd                                       3.002275e-05 1.789416e-05
## pos_35_pd                                       8.455787e-06 1.461402e-05
## pos_36_pd                                      -4.049895e-06 1.066027e-05
## pos_37_pd                                       2.117024e-05 1.508692e-05
## pos_38_pd                                       3.960634e-05 2.466409e-05
## pos_39_pd                                       6.397585e-05 3.344655e-05
## s(Time_Period_ID):as.factor(Region)Midwest.1   -1.775878e-05 3.661052e-06
## s(Time_Period_ID):as.factor(Region)Midwest.2   -1.289103e-05 2.760421e-06
## s(Time_Period_ID):as.factor(Region)Midwest.3    2.085494e-07 2.389289e-06
## s(Time_Period_ID):as.factor(Region)Midwest.4    1.122370e-05 2.500022e-06
## s(Time_Period_ID):as.factor(Region)Midwest.5    2.069662e-05 2.184618e-06
## s(Time_Period_ID):as.factor(Region)Midwest.6    3.142512e-05 2.509869e-06
## s(Time_Period_ID):as.factor(Region)Midwest.7    4.652513e-05 3.138207e-06
## s(Time_Period_ID):as.factor(Region)Midwest.8    7.225486e-05 5.032883e-06
## s(Time_Period_ID):as.factor(Region)Midwest.9    6.994333e-05 6.449222e-06
## s(Time_Period_ID):as.factor(Region)Northeast.1 -2.314621e-05 3.973050e-06
## s(Time_Period_ID):as.factor(Region)Northeast.2 -1.866289e-05 3.273368e-06
## s(Time_Period_ID):as.factor(Region)Northeast.3  4.393252e-06 3.057463e-06
## s(Time_Period_ID):as.factor(Region)Northeast.4  4.633969e-06 2.880762e-06
## s(Time_Period_ID):as.factor(Region)Northeast.5  8.806652e-06 3.204475e-06
## s(Time_Period_ID):as.factor(Region)Northeast.6  2.404534e-05 3.406465e-06
## s(Time_Period_ID):as.factor(Region)Northeast.7  6.582187e-05 4.877632e-06
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.168392e-04 5.528309e-06
## s(Time_Period_ID):as.factor(Region)Northeast.9  1.039955e-04 7.410729e-06
## s(Time_Period_ID):as.factor(Region)South.1     -2.081890e-05 3.325264e-06
## s(Time_Period_ID):as.factor(Region)South.2     -1.123259e-05 2.352751e-06
## s(Time_Period_ID):as.factor(Region)South.3      8.081093e-06 2.839123e-06
## s(Time_Period_ID):as.factor(Region)South.4      1.768916e-05 2.909781e-06
## s(Time_Period_ID):as.factor(Region)South.5      2.880856e-05 2.480828e-06
## s(Time_Period_ID):as.factor(Region)South.6      3.494430e-05 2.597782e-06
## s(Time_Period_ID):as.factor(Region)South.7      5.319637e-05 3.281626e-06
## s(Time_Period_ID):as.factor(Region)South.8      8.846831e-05 6.074756e-06
## s(Time_Period_ID):as.factor(Region)South.9      8.642540e-05 9.491102e-06
## s(Time_Period_ID):as.factor(Region)West.1      -1.290981e-05 2.309694e-06
## s(Time_Period_ID):as.factor(Region)West.2      -5.390325e-06 1.862185e-06
## s(Time_Period_ID):as.factor(Region)West.3       6.020627e-06 2.170083e-06
## s(Time_Period_ID):as.factor(Region)West.4       1.488210e-05 1.904864e-06
## s(Time_Period_ID):as.factor(Region)West.5       2.238901e-05 1.983359e-06
## s(Time_Period_ID):as.factor(Region)West.6       2.915617e-05 2.353027e-06
## s(Time_Period_ID):as.factor(Region)West.7       3.556922e-05 2.811635e-06
## s(Time_Period_ID):as.factor(Region)West.8       4.643359e-05 3.649901e-06
## s(Time_Period_ID):as.factor(Region)West.9       4.926954e-05 4.358096e-06

5.3.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx <- sensitivity_anlys_post_tx_sd_and_ci %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx$num_states <- sapply(plot_post_tx$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_vline(aes(xintercept = coef(main_analysis_model)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
  geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model)["Intervention_Redefined"]), y = 12, 
            x = coef(main_analysis_model)["Intervention_Redefined"] + 0.00001), color = "red")

  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

6 OLS Model Main Analysis With Fixed Time Effects

#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population

#fit an OLS with smoothed time effects
main_analysis_model_fixed_time<-lm(prop_dead~ State +
                           factor(Time_Period_ID) +
                           Naloxone_Pharmacy_Yes_Redefined +
                           Naloxone_Pharmacy_No_Redefined +
                           Medical_Marijuana_Redefined +
                           Recreational_Marijuana_Redefined +
                           GSL_Redefined +
                           PDMP_Redefined +
                           Medicaid_Expansion_Redefined +
                           Intervention_Redefined ,
                         data = main_analysis_data)

summary(main_analysis_model_fixed_time)
## 
## Call:
## lm(formula = prop_dead ~ State + factor(Time_Period_ID) + Naloxone_Pharmacy_Yes_Redefined + 
##     Naloxone_Pharmacy_No_Redefined + Medical_Marijuana_Redefined + 
##     Recreational_Marijuana_Redefined + GSL_Redefined + PDMP_Redefined + 
##     Medicaid_Expansion_Redefined + Intervention_Redefined, data = main_analysis_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.033e-04 -1.127e-05  2.730e-07  1.060e-05  1.329e-04 
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       2.690e-05  4.477e-06   6.008 2.25e-09 ***
## StateAlaska                      -4.545e-07  5.233e-06  -0.087 0.930802    
## StateArizona                      1.056e-05  4.810e-06   2.196 0.028199 *  
## StateArkansas                    -2.812e-05  4.749e-06  -5.922 3.77e-09 ***
## StateCalifornia                  -2.297e-05  5.226e-06  -4.395 1.17e-05 ***
## StateColorado                    -7.966e-06  5.206e-06  -1.530 0.126127    
## StateConnecticut                  1.233e-05  5.019e-06   2.457 0.014117 *  
## StateDelaware                     2.026e-05  4.829e-06   4.196 2.84e-05 ***
## StateFlorida                      1.477e-05  4.752e-06   3.107 0.001916 ** 
## StateGeorgia                     -6.738e-06  4.753e-06  -1.418 0.156481    
## StateHawaii                      -3.119e-05  5.155e-06  -6.050 1.74e-09 ***
## StateIdaho                       -7.178e-06  4.753e-06  -1.510 0.131165    
## StateIllinois                     2.423e-06  4.821e-06   0.503 0.615249    
## StateIndiana                      1.231e-05  4.727e-06   2.605 0.009264 ** 
## StateIowa                        -3.167e-05  4.738e-06  -6.684 3.04e-11 ***
## StateKansas                      -1.520e-05  4.703e-06  -3.231 0.001256 ** 
## StateKentucky                     5.787e-05  4.759e-06  12.160  < 2e-16 ***
## StateLouisiana                    2.101e-05  4.698e-06   4.472 8.20e-06 ***
## StateMaine                        2.151e-06  5.217e-06   0.412 0.680224    
## StateMaryland                    -5.345e-05  4.810e-06 -11.111  < 2e-16 ***
## StateMassachusetts                1.973e-05  4.784e-06   4.125 3.87e-05 ***
## StateMichigan                    -5.122e-07  4.853e-06  -0.106 0.915949    
## StateMinnesota                   -4.436e-05  4.934e-06  -8.992  < 2e-16 ***
## StateMississippi                 -6.311e-06  4.701e-06  -1.342 0.179598    
## StateMissouri                     8.772e-06  4.858e-06   1.806 0.071105 .  
## StateMontana                     -3.690e-05  4.968e-06  -7.428 1.66e-13 ***
## StateNebraska                    -3.727e-05  4.777e-06  -7.803 9.88e-15 ***
## StateNevada                       2.442e-05  5.062e-06   4.823 1.53e-06 ***
## StateNew Hampshire                1.473e-05  4.771e-06   3.087 0.002050 ** 
## StateNew Jersey                   3.229e-06  4.816e-06   0.671 0.502590    
## StateNew Mexico                   4.375e-05  5.128e-06   8.530  < 2e-16 ***
## StateNew York                    -1.106e-05  4.854e-06  -2.279 0.022773 *  
## StateNorth Carolina               1.177e-05  4.689e-06   2.509 0.012188 *  
## StateNorth Dakota                -4.407e-05  4.731e-06  -9.315  < 2e-16 ***
## StateOhio                         4.235e-05  4.764e-06   8.891  < 2e-16 ***
## StateOklahoma                     3.111e-05  4.732e-06   6.575 6.27e-11 ***
## StateOregon                      -3.003e-05  5.188e-06  -5.788 8.33e-09 ***
## StatePennsylvania                 4.396e-05  4.757e-06   9.240  < 2e-16 ***
## StateRhode Island                 1.390e-05  4.914e-06   2.829 0.004725 ** 
## StateSouth Carolina               1.253e-05  4.727e-06   2.651 0.008097 ** 
## StateSouth Dakota                -3.960e-05  4.754e-06  -8.329  < 2e-16 ***
## StateTennessee                    3.433e-05  4.677e-06   7.340 3.15e-13 ***
## StateTexas                       -4.871e-06  4.751e-06  -1.025 0.305395    
## StateUtah                         3.050e-06  4.705e-06   0.648 0.516817    
## StateVermont                     -1.916e-05  4.922e-06  -3.892 0.000103 ***
## StateVirginia                    -3.600e-06  4.698e-06  -0.766 0.443607    
## StateWashington                  -1.092e-05  5.268e-06  -2.073 0.038334 *  
## StateWest Virginia                8.857e-05  4.757e-06  18.617  < 2e-16 ***
## StateWisconsin                   -1.369e-06  4.708e-06  -0.291 0.771148    
## StateWyoming                      5.620e-07  4.702e-06   0.120 0.904871    
## factor(Time_Period_ID)2          -9.184e-07  4.177e-06  -0.220 0.826005    
## factor(Time_Period_ID)3           1.447e-06  4.179e-06   0.346 0.729219    
## factor(Time_Period_ID)4           3.163e-06  4.181e-06   0.756 0.449452    
## factor(Time_Period_ID)5           8.631e-06  4.183e-06   2.064 0.039193 *  
## factor(Time_Period_ID)6           9.444e-06  4.187e-06   2.255 0.024226 *  
## factor(Time_Period_ID)7           1.471e-05  4.189e-06   3.512 0.000455 ***
## factor(Time_Period_ID)8           1.452e-05  4.192e-06   3.465 0.000543 ***
## factor(Time_Period_ID)9           1.750e-05  4.198e-06   4.168 3.21e-05 ***
## factor(Time_Period_ID)10          1.699e-05  4.208e-06   4.036 5.65e-05 ***
## factor(Time_Period_ID)11          2.134e-05  4.217e-06   5.061 4.56e-07 ***
## factor(Time_Period_ID)12          2.224e-05  4.238e-06   5.247 1.72e-07 ***
## factor(Time_Period_ID)13          3.016e-05  4.251e-06   7.094 1.83e-12 ***
## factor(Time_Period_ID)14          3.341e-05  4.269e-06   7.827 8.23e-15 ***
## factor(Time_Period_ID)15          3.514e-05  4.269e-06   8.230 3.43e-16 ***
## factor(Time_Period_ID)16          3.590e-05  4.288e-06   8.373  < 2e-16 ***
## factor(Time_Period_ID)17          4.012e-05  4.325e-06   9.277  < 2e-16 ***
## factor(Time_Period_ID)18          3.897e-05  4.345e-06   8.969  < 2e-16 ***
## factor(Time_Period_ID)19          3.949e-05  4.361e-06   9.055  < 2e-16 ***
## factor(Time_Period_ID)20          3.882e-05  4.388e-06   8.848  < 2e-16 ***
## factor(Time_Period_ID)21          4.242e-05  4.411e-06   9.617  < 2e-16 ***
## factor(Time_Period_ID)22          4.040e-05  4.443e-06   9.092  < 2e-16 ***
## factor(Time_Period_ID)23          4.922e-05  4.461e-06  11.034  < 2e-16 ***
## factor(Time_Period_ID)24          4.817e-05  4.511e-06  10.679  < 2e-16 ***
## factor(Time_Period_ID)25          4.778e-05  4.527e-06  10.555  < 2e-16 ***
## factor(Time_Period_ID)26          4.763e-05  4.552e-06  10.463  < 2e-16 ***
## factor(Time_Period_ID)27          5.359e-05  4.597e-06  11.657  < 2e-16 ***
## factor(Time_Period_ID)28          5.148e-05  4.644e-06  11.086  < 2e-16 ***
## factor(Time_Period_ID)29          5.252e-05  4.703e-06  11.169  < 2e-16 ***
## factor(Time_Period_ID)30          5.345e-05  4.787e-06  11.166  < 2e-16 ***
## factor(Time_Period_ID)31          6.133e-05  4.834e-06  12.686  < 2e-16 ***
## factor(Time_Period_ID)32          6.292e-05  5.050e-06  12.460  < 2e-16 ***
## factor(Time_Period_ID)33          7.678e-05  5.153e-06  14.900  < 2e-16 ***
## factor(Time_Period_ID)34          8.123e-05  5.361e-06  15.153  < 2e-16 ***
## factor(Time_Period_ID)35          8.909e-05  5.424e-06  16.426  < 2e-16 ***
## factor(Time_Period_ID)36          8.729e-05  5.524e-06  15.801  < 2e-16 ***
## factor(Time_Period_ID)37          8.433e-05  5.528e-06  15.254  < 2e-16 ***
## factor(Time_Period_ID)38          8.291e-05  5.553e-06  14.931  < 2e-16 ***
## factor(Time_Period_ID)39          8.255e-05  5.570e-06  14.822  < 2e-16 ***
## factor(Time_Period_ID)40          9.261e-05  5.576e-06  16.608  < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined  -1.490e-06  3.098e-06  -0.481 0.630612    
## Naloxone_Pharmacy_No_Redefined   -1.381e-06  2.633e-06  -0.525 0.599951    
## Medical_Marijuana_Redefined       2.002e-05  2.074e-06   9.654  < 2e-16 ***
## Recreational_Marijuana_Redefined -1.896e-05  3.136e-06  -6.047 1.77e-09 ***
## GSL_Redefined                     6.260e-06  2.199e-06   2.847 0.004464 ** 
## PDMP_Redefined                   -1.397e-05  1.744e-06  -8.009 2.00e-15 ***
## Medicaid_Expansion_Redefined      1.238e-05  2.148e-06   5.761 9.75e-09 ***
## Intervention_Redefined           -3.057e-07  1.705e-06  -0.179 0.857773    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.088e-05 on 1903 degrees of freedom
## Multiple R-squared:  0.8009, Adjusted R-squared:  0.7908 
## F-statistic: 79.72 on 96 and 1903 DF,  p-value: < 2.2e-16
#examine fitted values
summary(fitted(main_analysis_model_fixed_time))
##       Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
## -2.746e-05  4.210e-05  6.466e-05  6.974e-05  9.474e-05  2.310e-04
hist(fitted(main_analysis_model_fixed_time))

par(mfrow = c(2,2))
plot(main_analysis_model_fixed_time)

6.1 Coefficients and 95% CI

#compute the full dataset including basis functions
full_df_w_basis_functions_fixed_time <- model.matrix(main_analysis_model_fixed_time)

#estimate the 95% CI and SD
coefficient_values_fixed_time <- coef(main_analysis_model_fixed_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_fixed_time <- compute_sd_and_CI(full_df_w_basis_functions_fixed_time, main_analysis_data$prop_dead,
                                             coefficient_values_fixed_time, 
                                             p = ncol(full_df_w_basis_functions_fixed_time) - 50)
main_analysis_sd_and_ci_fixed_time
##                                        lb_coef   coef_values       ub_coef
## (Intercept)                       1.942733e-05  2.689875e-05  3.437016e-05
## StateAlaska                      -8.915125e-06 -4.544863e-07  8.006152e-06
## StateArizona                      4.074649e-06  1.056466e-05  1.705466e-05
## StateArkansas                    -3.522119e-05 -2.812388e-05 -2.102657e-05
## StateCalifornia                  -3.182303e-05 -2.296838e-05 -1.411373e-05
## StateColorado                    -1.540614e-05 -7.966278e-06 -5.264136e-07
## StateConnecticut                  3.982240e-06  1.233036e-05  2.067849e-05
## StateDelaware                     6.618517e-06  2.026181e-05  3.390509e-05
## StateFlorida                      9.082273e-06  1.476651e-05  2.045074e-05
## StateGeorgia                     -1.184259e-05 -6.737520e-06 -1.632450e-06
## StateHawaii                      -3.925571e-05 -3.118831e-05 -2.312091e-05
## StateIdaho                       -1.303271e-05 -7.178278e-06 -1.323841e-06
## StateIllinois                    -4.479242e-06  2.423321e-06  9.325884e-06
## StateIndiana                      6.627081e-06  1.231332e-05  1.799956e-05
## StateIowa                        -3.776189e-05 -3.167392e-05 -2.558595e-05
## StateKansas                      -2.080300e-05 -1.519561e-05 -9.588212e-06
## StateKentucky                     4.987862e-05  5.786783e-05  6.585705e-05
## StateLouisiana                    1.503427e-05  2.100942e-05  2.698456e-05
## StateMaine                       -8.073911e-06  2.150682e-06  1.237528e-05
## StateMaryland                    -6.062060e-05 -5.344500e-05 -4.626940e-05
## StateMassachusetts                9.652271e-06  1.973098e-05  2.980970e-05
## StateMichigan                    -6.180377e-06 -5.122307e-07  5.155916e-06
## StateMinnesota                   -5.227065e-05 -4.436410e-05 -3.645755e-05
## StateMississippi                 -1.254397e-05 -6.310813e-06 -7.765172e-08
## StateMissouri                     3.200968e-06  8.772120e-06  1.434327e-05
## StateMontana                     -4.651537e-05 -3.690314e-05 -2.729090e-05
## StateNebraska                    -4.321365e-05 -3.727356e-05 -3.133347e-05
## StateNevada                       1.617230e-05  2.441663e-05  3.266096e-05
## StateNew Hampshire                4.892681e-06  1.473038e-05  2.456807e-05
## StateNew Jersey                  -6.275080e-06  3.229125e-06  1.273333e-05
## StateNew Mexico                   3.364025e-05  4.374662e-05  5.385300e-05
## StateNew York                    -1.767349e-05 -1.106203e-05 -4.450582e-06
## StateNorth Carolina               6.891922e-06  1.176628e-05  1.664063e-05
## StateNorth Dakota                -5.190478e-05 -4.406765e-05 -3.623052e-05
## StateOhio                         2.948539e-05  4.235447e-05  5.522355e-05
## StateOklahoma                     2.275446e-05  3.111254e-05  3.947062e-05
## StateOregon                      -3.780289e-05 -3.002854e-05 -2.225418e-05
## StatePennsylvania                 3.560202e-05  4.395971e-05  5.231739e-05
## StateRhode Island                 4.021211e-06  1.389934e-05  2.377747e-05
## StateSouth Carolina               7.170290e-06  1.252918e-05  1.788807e-05
## StateSouth Dakota                -4.569666e-05 -3.959801e-05 -3.349937e-05
## StateTennessee                    2.739848e-05  3.433253e-05  4.126657e-05
## StateTexas                       -1.177957e-05 -4.870736e-06  2.038100e-06
## StateUtah                        -3.448839e-06  3.050429e-06  9.549696e-06
## StateVermont                     -2.680727e-05 -1.915904e-05 -1.151081e-05
## StateVirginia                    -8.353641e-06 -3.600273e-06  1.153096e-06
## StateWashington                  -1.902188e-05 -1.091934e-05 -2.816797e-06
## StateWest Virginia                7.077605e-05  8.856911e-05  1.063622e-04
## StateWisconsin                   -6.304741e-06 -1.369527e-06  3.565686e-06
## StateWyoming                     -6.603788e-06  5.619765e-07  7.727741e-06
## factor(Time_Period_ID)2          -9.692754e-06 -9.184054e-07  7.855943e-06
## factor(Time_Period_ID)3          -7.047547e-06  1.446718e-06  9.940982e-06
## factor(Time_Period_ID)4          -5.373015e-06  3.162920e-06  1.169886e-05
## factor(Time_Period_ID)5           8.373942e-08  8.631266e-06  1.717879e-05
## factor(Time_Period_ID)6           1.116986e-06  9.443451e-06  1.776991e-05
## factor(Time_Period_ID)7           6.580302e-06  1.471081e-05  2.284132e-05
## factor(Time_Period_ID)8           6.383961e-06  1.452315e-05  2.266234e-05
## factor(Time_Period_ID)9           9.623193e-06  1.749862e-05  2.537405e-05
## factor(Time_Period_ID)10          9.060379e-06  1.698551e-05  2.491065e-05
## factor(Time_Period_ID)11          1.368192e-05  2.134289e-05  2.900385e-05
## factor(Time_Period_ID)12          1.368767e-05  2.223594e-05  3.078422e-05
## factor(Time_Period_ID)13          2.242234e-05  3.015936e-05  3.789639e-05
## factor(Time_Period_ID)14          2.570222e-05  3.341473e-05  4.112724e-05
## factor(Time_Period_ID)15          2.721862e-05  3.513515e-05  4.305168e-05
## factor(Time_Period_ID)16          2.816967e-05  3.590147e-05  4.363327e-05
## factor(Time_Period_ID)17          3.208377e-05  4.012433e-05  4.816490e-05
## factor(Time_Period_ID)18          3.124511e-05  3.897322e-05  4.670133e-05
## factor(Time_Period_ID)19          3.001830e-05  3.949054e-05  4.896278e-05
## factor(Time_Period_ID)20          3.032985e-05  3.882449e-05  4.731914e-05
## factor(Time_Period_ID)21          3.435043e-05  4.242025e-05  5.049006e-05
## factor(Time_Period_ID)22          3.206191e-05  4.039724e-05  4.873257e-05
## factor(Time_Period_ID)23          4.086600e-05  4.921866e-05  5.757132e-05
## factor(Time_Period_ID)24          3.958479e-05  4.817116e-05  5.675754e-05
## factor(Time_Period_ID)25          3.915444e-05  4.777880e-05  5.640317e-05
## factor(Time_Period_ID)26          3.905132e-05  4.763090e-05  5.621049e-05
## factor(Time_Period_ID)27          4.498689e-05  5.359093e-05  6.219497e-05
## factor(Time_Period_ID)28          4.272095e-05  5.148042e-05  6.023988e-05
## factor(Time_Period_ID)29          4.342132e-05  5.252397e-05  6.162661e-05
## factor(Time_Period_ID)30          4.394029e-05  5.345100e-05  6.296171e-05
## factor(Time_Period_ID)31          5.164047e-05  6.132752e-05  7.101457e-05
## factor(Time_Period_ID)32          5.274482e-05  6.292231e-05  7.309981e-05
## factor(Time_Period_ID)33          6.548020e-05  7.678000e-05  8.807980e-05
## factor(Time_Period_ID)34          6.863541e-05  8.123049e-05  9.382557e-05
## factor(Time_Period_ID)35          7.464630e-05  8.908675e-05  1.035272e-04
## factor(Time_Period_ID)36          7.410766e-05  8.729149e-05  1.004753e-04
## factor(Time_Period_ID)37          7.178644e-05  8.432596e-05  9.686548e-05
## factor(Time_Period_ID)38          6.975402e-05  8.290643e-05  9.605884e-05
## factor(Time_Period_ID)39          7.019997e-05  8.255097e-05  9.490197e-05
## factor(Time_Period_ID)40          7.899652e-05  9.261112e-05  1.062257e-04
## Naloxone_Pharmacy_Yes_Redefined  -7.593619e-06 -1.490078e-06  4.613463e-06
## Naloxone_Pharmacy_No_Redefined   -6.103208e-06 -1.381355e-06  3.340499e-06
## Medical_Marijuana_Redefined       1.500898e-05  2.002227e-05  2.503556e-05
## Recreational_Marijuana_Redefined -2.730819e-05 -1.896470e-05 -1.062121e-05
## GSL_Redefined                     1.774296e-06  6.260311e-06  1.074632e-05
## PDMP_Redefined                   -1.726427e-05 -1.396633e-05 -1.066840e-05
## Medicaid_Expansion_Redefined      7.892999e-06  1.237642e-05  1.685984e-05
## Intervention_Redefined           -3.648105e-06 -3.056590e-07  3.036787e-06
##                                       sd_coef
## (Intercept)                      3.811947e-06
## StateAlaska                      4.316652e-06
## StateArizona                     3.311228e-06
## StateArkansas                    3.621075e-06
## StateCalifornia                  4.517678e-06
## StateColorado                    3.795849e-06
## StateConnecticut                 4.259247e-06
## StateDelaware                    6.960861e-06
## StateFlorida                     2.900120e-06
## StateGeorgia                     2.604628e-06
## StateHawaii                      4.116019e-06
## StateIdaho                       2.986957e-06
## StateIllinois                    3.521716e-06
## StateIndiana                     2.901142e-06
## StateIowa                        3.106108e-06
## StateKansas                      2.860916e-06
## StateKentucky                    4.076130e-06
## StateLouisiana                   3.048543e-06
## StateMaine                       5.216629e-06
## StateMaryland                    3.661021e-06
## StateMassachusetts               5.142200e-06
## StateMichigan                    2.891912e-06
## StateMinnesota                   4.033952e-06
## StateMississippi                 3.180184e-06
## StateMissouri                    2.842424e-06
## StateMontana                     4.904200e-06
## StateNebraska                    3.030658e-06
## StateNevada                      4.206289e-06
## StateNew Hampshire               5.019232e-06
## StateNew Jersey                  4.849084e-06
## StateNew Mexico                  5.156316e-06
## StateNew York                    3.373190e-06
## StateNorth Carolina              2.486916e-06
## StateNorth Dakota                3.998535e-06
## StateOhio                        6.565857e-06
## StateOklahoma                    4.264327e-06
## StateOregon                      3.966506e-06
## StatePennsylvania                4.264124e-06
## StateRhode Island                5.039861e-06
## StateSouth Carolina              2.734127e-06
## StateSouth Dakota                3.111554e-06
## StateTennessee                   3.537777e-06
## StateTexas                       3.524916e-06
## StateUtah                        3.315953e-06
## StateVermont                     3.902157e-06
## StateVirginia                    2.425188e-06
## StateWashington                  4.133950e-06
## StateWest Virginia               9.078091e-06
## StateWisconsin                   2.517966e-06
## StateWyoming                     3.656002e-06
## factor(Time_Period_ID)2          4.476708e-06
## factor(Time_Period_ID)3          4.333808e-06
## factor(Time_Period_ID)4          4.355069e-06
## factor(Time_Period_ID)5          4.360983e-06
## factor(Time_Period_ID)6          4.248196e-06
## factor(Time_Period_ID)7          4.148219e-06
## factor(Time_Period_ID)8          4.152649e-06
## factor(Time_Period_ID)9          4.018075e-06
## factor(Time_Period_ID)10         4.043436e-06
## factor(Time_Period_ID)11         3.908654e-06
## factor(Time_Period_ID)12         4.361364e-06
## factor(Time_Period_ID)13         3.947461e-06
## factor(Time_Period_ID)14         3.934954e-06
## factor(Time_Period_ID)15         4.039045e-06
## factor(Time_Period_ID)16         3.944795e-06
## factor(Time_Period_ID)17         4.102330e-06
## factor(Time_Period_ID)18         3.942913e-06
## factor(Time_Period_ID)19         4.832778e-06
## factor(Time_Period_ID)20         4.334003e-06
## factor(Time_Period_ID)21         4.117252e-06
## factor(Time_Period_ID)22         4.252720e-06
## factor(Time_Period_ID)23         4.261559e-06
## factor(Time_Period_ID)24         4.380804e-06
## factor(Time_Period_ID)25         4.400185e-06
## factor(Time_Period_ID)26         4.377339e-06
## factor(Time_Period_ID)27         4.389815e-06
## factor(Time_Period_ID)28         4.469113e-06
## factor(Time_Period_ID)29         4.644206e-06
## factor(Time_Period_ID)30         4.852404e-06
## factor(Time_Period_ID)31         4.942374e-06
## factor(Time_Period_ID)32         5.192600e-06
## factor(Time_Period_ID)33         5.765205e-06
## factor(Time_Period_ID)34         6.426063e-06
## factor(Time_Period_ID)35         7.367576e-06
## factor(Time_Period_ID)36         6.726444e-06
## factor(Time_Period_ID)37         6.397712e-06
## factor(Time_Period_ID)38         6.710412e-06
## factor(Time_Period_ID)39         6.301531e-06
## factor(Time_Period_ID)40         6.946221e-06
## Naloxone_Pharmacy_Yes_Redefined  3.114052e-06
## Naloxone_Pharmacy_No_Redefined   2.409109e-06
## Medical_Marijuana_Redefined      2.557800e-06
## Recreational_Marijuana_Redefined 4.256882e-06
## GSL_Redefined                    2.288783e-06
## PDMP_Redefined                   1.682619e-06
## Medicaid_Expansion_Redefined     2.287460e-06
## Intervention_Redefined           1.705330e-06

6.2 Event Study

6.2.1 Model Fitting

#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures, 
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention

formula_event_study_fixed_time <- formula(paste("prop_dead ~ State +
                                           factor(Time_Period_ID)  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2), 
                                            function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
                                     "+",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_fixed_time<-lm(formula_event_study_fixed_time,
                                         data = sensitivity_anlys_event_study_data)

summary(sensitivity_anlys_event_study_model_fixed_time)
## 
## Call:
## lm(formula = formula_event_study_fixed_time, data = sensitivity_anlys_event_study_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.003e-04 -1.170e-05 -1.240e-07  1.090e-05  1.303e-04 
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       4.907e-05  6.564e-06   7.476 1.18e-13 ***
## StateAlaska                       1.998e-05  6.873e-06   2.907 0.003696 ** 
## StateArizona                      2.229e-05  5.367e-06   4.153 3.43e-05 ***
## StateArkansas                    -2.006e-05  5.051e-06  -3.973 7.39e-05 ***
## StateCalifornia                  -3.474e-05  6.131e-06  -5.666 1.70e-08 ***
## StateColorado                     3.005e-06  5.618e-06   0.535 0.592762    
## StateConnecticut                  1.245e-05  5.003e-06   2.488 0.012923 *  
## StateDelaware                     4.009e-05  6.603e-06   6.071 1.54e-09 ***
## StateFlorida                     -1.064e-06  6.058e-06  -0.176 0.860542    
## StateGeorgia                     -2.555e-05  6.454e-06  -3.959 7.81e-05 ***
## StateHawaii                      -2.821e-05  6.053e-06  -4.662 3.36e-06 ***
## StateIdaho                        1.148e-05  6.252e-06   1.836 0.066493 .  
## StateIllinois                    -9.164e-06  5.580e-06  -1.642 0.100721    
## StateIndiana                      1.741e-05  4.825e-06   3.608 0.000316 ***
## StateIowa                        -3.869e-05  5.117e-06  -7.561 6.30e-14 ***
## StateKansas                      -1.617e-05  4.692e-06  -3.446 0.000583 ***
## StateKentucky                     6.685e-05  5.095e-06  13.119  < 2e-16 ***
## StateLouisiana                    1.262e-05  5.170e-06   2.441 0.014721 *  
## StateMaine                        7.622e-06  5.281e-06   1.443 0.149083    
## StateMaryland                    -6.648e-05  5.664e-06 -11.738  < 2e-16 ***
## StateMassachusetts                2.074e-05  4.761e-06   4.357 1.39e-05 ***
## StateMichigan                    -3.460e-06  4.991e-06  -0.693 0.488258    
## StateMinnesota                   -4.472e-05  4.923e-06  -9.084  < 2e-16 ***
## StateMississippi                  9.347e-06  5.837e-06   1.601 0.109482    
## StateMissouri                     2.742e-06  5.067e-06   0.541 0.588448    
## StateMontana                     -4.400e-05  5.384e-06  -8.173 5.54e-16 ***
## StateNebraska                    -2.520e-05  5.423e-06  -4.647 3.62e-06 ***
## StateNevada                       2.225e-05  5.176e-06   4.298 1.81e-05 ***
## StateNew Hampshire                1.920e-05  4.858e-06   3.953 8.01e-05 ***
## StateNew Jersey                  -9.100e-06  5.637e-06  -1.614 0.106631    
## StateNew Mexico                   4.972e-05  5.257e-06   9.457  < 2e-16 ***
## StateNew York                    -1.123e-05  4.837e-06  -2.322 0.020329 *  
## StateNorth Carolina               6.032e-06  4.934e-06   1.223 0.221662    
## StateNorth Dakota                -3.190e-05  5.395e-06  -5.913 3.99e-09 ***
## StateOhio                         2.432e-05  6.449e-06   3.771 0.000168 ***
## StateOklahoma                     3.991e-05  5.013e-06   7.963 2.93e-15 ***
## StateOregon                      -2.465e-05  5.279e-06  -4.671 3.22e-06 ***
## StatePennsylvania                 2.898e-05  6.030e-06   4.806 1.67e-06 ***
## StateRhode Island                 3.009e-05  5.947e-06   5.060 4.61e-07 ***
## StateSouth Carolina               3.160e-05  6.357e-06   4.972 7.25e-07 ***
## StateSouth Dakota                -1.975e-05  6.566e-06  -3.008 0.002668 ** 
## StateTennessee                    3.461e-05  4.652e-06   7.441 1.53e-13 ***
## StateTexas                       -1.812e-05  5.845e-06  -3.101 0.001958 ** 
## StateUtah                        -8.579e-07  4.856e-06  -0.177 0.859781    
## StateVermont                     -1.440e-05  4.996e-06  -2.881 0.004007 ** 
## StateVirginia                    -1.259e-05  5.251e-06  -2.397 0.016640 *  
## StateWashington                  -8.078e-06  5.277e-06  -1.531 0.126024    
## StateWest Virginia                1.014e-04  5.442e-06  18.630  < 2e-16 ***
## StateWisconsin                   -9.904e-06  5.179e-06  -1.912 0.055983 .  
## StateWyoming                      4.817e-06  4.754e-06   1.013 0.310987    
## factor(Time_Period_ID)2          -1.226e-06  4.294e-06  -0.285 0.775335    
## factor(Time_Period_ID)3          -7.060e-07  4.340e-06  -0.163 0.870809    
## factor(Time_Period_ID)4          -2.624e-07  4.297e-06  -0.061 0.951315    
## factor(Time_Period_ID)5           3.820e-06  4.386e-06   0.871 0.383928    
## factor(Time_Period_ID)6           3.189e-06  4.450e-06   0.717 0.473747    
## factor(Time_Period_ID)7           7.371e-06  4.491e-06   1.641 0.100931    
## factor(Time_Period_ID)8           6.092e-06  4.593e-06   1.326 0.184849    
## factor(Time_Period_ID)9           8.252e-06  4.684e-06   1.762 0.078257 .  
## factor(Time_Period_ID)10          6.567e-06  4.802e-06   1.368 0.171589    
## factor(Time_Period_ID)11          9.902e-06  4.927e-06   2.010 0.044593 *  
## factor(Time_Period_ID)12          9.748e-06  5.059e-06   1.927 0.054144 .  
## factor(Time_Period_ID)13          1.670e-05  5.200e-06   3.210 0.001348 ** 
## factor(Time_Period_ID)14          1.854e-05  5.360e-06   3.460 0.000553 ***
## factor(Time_Period_ID)15          1.881e-05  5.507e-06   3.416 0.000650 ***
## factor(Time_Period_ID)16          1.899e-05  5.659e-06   3.356 0.000807 ***
## factor(Time_Period_ID)17          2.225e-05  5.855e-06   3.800 0.000150 ***
## factor(Time_Period_ID)18          1.950e-05  6.032e-06   3.233 0.001245 ** 
## factor(Time_Period_ID)19          1.945e-05  6.206e-06   3.134 0.001751 ** 
## factor(Time_Period_ID)20          1.735e-05  6.414e-06   2.705 0.006900 ** 
## factor(Time_Period_ID)21          1.963e-05  6.612e-06   2.969 0.003027 ** 
## factor(Time_Period_ID)22          1.700e-05  6.804e-06   2.498 0.012578 *  
## factor(Time_Period_ID)23          2.441e-05  7.016e-06   3.479 0.000515 ***
## factor(Time_Period_ID)24          2.277e-05  7.230e-06   3.149 0.001662 ** 
## factor(Time_Period_ID)25          2.236e-05  7.438e-06   3.006 0.002680 ** 
## factor(Time_Period_ID)26          2.074e-05  7.653e-06   2.710 0.006783 ** 
## factor(Time_Period_ID)27          2.614e-05  7.869e-06   3.322 0.000911 ***
## factor(Time_Period_ID)28          2.343e-05  8.087e-06   2.898 0.003805 ** 
## factor(Time_Period_ID)29          2.232e-05  8.412e-06   2.653 0.008038 ** 
## factor(Time_Period_ID)30          2.271e-05  8.657e-06   2.624 0.008772 ** 
## factor(Time_Period_ID)31          2.929e-05  8.898e-06   3.292 0.001015 ** 
## factor(Time_Period_ID)32          2.949e-05  9.193e-06   3.208 0.001360 ** 
## factor(Time_Period_ID)33          4.277e-05  9.468e-06   4.517 6.66e-06 ***
## factor(Time_Period_ID)34          4.539e-05  9.764e-06   4.648 3.59e-06 ***
## factor(Time_Period_ID)35          5.177e-05  9.984e-06   5.185 2.39e-07 ***
## factor(Time_Period_ID)36          4.976e-05  1.026e-05   4.850 1.34e-06 ***
## factor(Time_Period_ID)37          4.494e-05  1.049e-05   4.285 1.92e-05 ***
## factor(Time_Period_ID)38          4.171e-05  1.073e-05   3.888 0.000105 ***
## factor(Time_Period_ID)39          4.081e-05  1.098e-05   3.716 0.000209 ***
## factor(Time_Period_ID)40          4.924e-05  1.120e-05   4.395 1.17e-05 ***
## Naloxone_Pharmacy_Yes_Redefined  -1.607e-06  3.116e-06  -0.516 0.606125    
## Naloxone_Pharmacy_No_Redefined   -2.293e-06  2.654e-06  -0.864 0.387651    
## Medical_Marijuana_Redefined       1.771e-05  2.116e-06   8.371  < 2e-16 ***
## Recreational_Marijuana_Redefined -2.063e-05  3.176e-06  -6.496 1.06e-10 ***
## GSL_Redefined                     7.828e-06  2.209e-06   3.545 0.000403 ***
## PDMP_Redefined                   -1.628e-05  1.773e-06  -9.183  < 2e-16 ***
## Medicaid_Expansion_Redefined      1.417e-05  2.183e-06   6.491 1.09e-10 ***
## neg_2_pd                         -6.703e-07  4.323e-06  -0.155 0.876786    
## neg_3_pd                         -1.008e-06  4.398e-06  -0.229 0.818725    
## neg_4_pd                         -4.528e-06  4.454e-06  -1.017 0.309477    
## neg_5_pd                         -7.417e-06  4.513e-06  -1.643 0.100464    
## neg_6_pd                         -8.528e-06  4.666e-06  -1.828 0.067732 .  
## neg_7_pd                         -1.275e-05  4.728e-06  -2.696 0.007081 ** 
## neg_8_pd                         -1.567e-05  4.847e-06  -3.233 0.001246 ** 
## neg_9_pd                         -1.311e-05  5.036e-06  -2.603 0.009329 ** 
## neg_10_pd                        -1.458e-05  5.190e-06  -2.809 0.005023 ** 
## neg_11_pd                        -1.527e-05  5.354e-06  -2.852 0.004398 ** 
## neg_12_pd                        -1.346e-05  5.651e-06  -2.383 0.017296 *  
## neg_13_pd                        -1.744e-05  5.789e-06  -3.012 0.002631 ** 
## neg_14_pd                        -1.934e-05  5.941e-06  -3.255 0.001153 ** 
## neg_15_pd                        -2.439e-05  6.081e-06  -4.011 6.30e-05 ***
## neg_16_pd                        -2.572e-05  6.361e-06  -4.044 5.47e-05 ***
## neg_17_pd                        -2.762e-05  6.771e-06  -4.080 4.71e-05 ***
## neg_18_pd                        -2.993e-05  6.988e-06  -4.283 1.94e-05 ***
## neg_19_pd                        -3.146e-05  7.204e-06  -4.367 1.33e-05 ***
## neg_20_pd                        -3.532e-05  7.647e-06  -4.619 4.13e-06 ***
## neg_21_pd                        -3.583e-05  8.143e-06  -4.400 1.14e-05 ***
## neg_22_pd                        -3.694e-05  8.297e-06  -4.453 9.00e-06 ***
## neg_23_pd                        -3.407e-05  8.606e-06  -3.959 7.80e-05 ***
## neg_24_pd                        -3.829e-05  9.272e-06  -4.129 3.81e-05 ***
## neg_25_pd                        -3.708e-05  9.431e-06  -3.932 8.76e-05 ***
## neg_26_pd                        -3.563e-05  9.804e-06  -3.634 0.000287 ***
## neg_27_pd                        -3.538e-05  1.093e-05  -3.237 0.001230 ** 
## neg_28_pd                        -3.613e-05  1.108e-05  -3.261 0.001130 ** 
## neg_29_pd                        -3.344e-05  1.173e-05  -2.851 0.004406 ** 
## neg_30_pd                        -3.654e-05  1.252e-05  -2.918 0.003562 ** 
## neg_31_pd                        -3.942e-05  1.266e-05  -3.113 0.001880 ** 
## neg_32_pd                        -4.412e-05  1.367e-05  -3.227 0.001271 ** 
## neg_33_pd                        -3.873e-05  1.737e-05  -2.229 0.025943 *  
## pos_0_pd                          5.034e-07  4.305e-06   0.117 0.906915    
## pos_1_pd                         -5.834e-07  4.349e-06  -0.134 0.893316    
## pos_2_pd                          3.351e-06  4.369e-06   0.767 0.443194    
## pos_3_pd                          2.686e-06  4.452e-06   0.603 0.546407    
## pos_4_pd                          4.165e-06  4.529e-06   0.920 0.357853    
## pos_5_pd                          2.911e-06  4.621e-06   0.630 0.528715    
## pos_6_pd                          5.521e-06  4.749e-06   1.163 0.245110    
## pos_7_pd                          4.642e-06  4.871e-06   0.953 0.340755    
## pos_8_pd                          4.601e-06  5.063e-06   0.909 0.363596    
## pos_9_pd                          5.122e-06  5.229e-06   0.979 0.327482    
## pos_10_pd                         5.693e-06  5.362e-06   1.062 0.288514    
## pos_11_pd                         6.550e-06  5.546e-06   1.181 0.237761    
## pos_12_pd                         9.126e-06  5.736e-06   1.591 0.111772    
## pos_13_pd                         6.685e-06  5.903e-06   1.132 0.257583    
## pos_14_pd                         9.568e-06  6.146e-06   1.557 0.119695    
## pos_15_pd                         9.314e-06  6.374e-06   1.461 0.144126    
## pos_16_pd                         9.564e-06  6.558e-06   1.459 0.144863    
## pos_17_pd                         1.345e-05  6.826e-06   1.970 0.048991 *  
## pos_18_pd                         1.669e-05  7.064e-06   2.362 0.018286 *  
## pos_19_pd                         1.767e-05  7.240e-06   2.440 0.014779 *  
## pos_20_pd                         1.843e-05  7.535e-06   2.446 0.014522 *  
## pos_21_pd                         1.837e-05  7.842e-06   2.343 0.019247 *  
## pos_22_pd                         1.932e-05  8.080e-06   2.391 0.016921 *  
## pos_23_pd                         1.877e-05  8.342e-06   2.250 0.024536 *  
## pos_24_pd                         1.212e-05  8.745e-06   1.386 0.165857    
## pos_25_pd                         1.599e-05  9.122e-06   1.753 0.079809 .  
## pos_26_pd                         1.866e-05  9.337e-06   1.998 0.045816 *  
## pos_27_pd                         1.653e-05  9.572e-06   1.727 0.084370 .  
## pos_28_pd                         2.006e-05  9.773e-06   2.052 0.040267 *  
## pos_29_pd                         2.107e-05  1.030e-05   2.045 0.040949 *  
## pos_30_pd                         2.695e-05  1.061e-05   2.540 0.011178 *  
## pos_31_pd                         3.953e-05  1.096e-05   3.606 0.000319 ***
## pos_32_pd                         4.049e-05  1.166e-05   3.474 0.000524 ***
## pos_33_pd                         4.292e-05  1.211e-05   3.544 0.000404 ***
## pos_34_pd                         4.819e-05  1.232e-05   3.911 9.53e-05 ***
## pos_35_pd                         3.798e-05  1.352e-05   2.809 0.005029 ** 
## pos_36_pd                         3.246e-05  1.372e-05   2.366 0.018067 *  
## pos_37_pd                         5.077e-05  1.528e-05   3.323 0.000908 ***
## pos_38_pd                         5.048e-05  1.882e-05   2.682 0.007391 ** 
## pos_39_pd                         4.850e-05  1.898e-05   2.556 0.010672 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.077e-05 on 1832 degrees of freedom
## Multiple R-squared:  0.8104, Adjusted R-squared:  0.7931 
## F-statistic: 46.89 on 167 and 1832 DF,  p-value: < 2.2e-16

6.2.2 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_fixed_time <- model.matrix(sensitivity_anlys_event_study_model_fixed_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_fixed_time <- coef(sensitivity_anlys_event_study_model_fixed_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_fixed_time <-
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_event_study_fixed_time), 
                    sensitivity_anlys_event_study_data$prop_dead,
                    coefficient_values_sensitivity_anlys_event_study_fixed_time,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_fixed_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_fixed_time)
##                                        lb_coef   coef_values       ub_coef
## (Intercept)                       3.918940e-05  4.907266e-05  5.895592e-05
## StateAlaska                       9.415737e-06  1.997777e-05  3.053979e-05
## StateArizona                      1.475688e-05  2.228880e-05  2.982073e-05
## StateArkansas                    -2.729612e-05 -2.006447e-05 -1.283281e-05
## StateCalifornia                  -4.438921e-05 -3.473672e-05 -2.508422e-05
## StateColorado                    -5.143242e-06  3.005253e-06  1.115375e-05
## StateConnecticut                  3.849098e-06  1.244969e-05  2.105028e-05
## StateDelaware                     2.544578e-05  4.008813e-05  5.473047e-05
## StateFlorida                     -8.585087e-06 -1.064421e-06  6.456245e-06
## StateGeorgia                     -3.377383e-05 -2.555180e-05 -1.732977e-05
## StateHawaii                      -3.577339e-05 -2.821460e-05 -2.065581e-05
## StateIdaho                        2.987889e-06  1.148011e-05  1.997232e-05
## StateIllinois                    -1.676018e-05 -9.163881e-06 -1.567580e-06
## StateIndiana                      1.175833e-05  1.741093e-05  2.306353e-05
## StateIowa                        -4.515825e-05 -3.869201e-05 -3.222577e-05
## StateKansas                      -2.184681e-05 -1.616568e-05 -1.048454e-05
## StateKentucky                     5.919587e-05  6.684508e-05  7.449429e-05
## StateLouisiana                    5.699910e-06  1.262372e-05  1.954753e-05
## StateMaine                       -3.068301e-06  7.622034e-06  1.831237e-05
## StateMaryland                    -7.455772e-05 -6.648083e-05 -5.840394e-05
## StateMassachusetts                1.055637e-05  2.074040e-05  3.092442e-05
## StateMichigan                    -9.237121e-06 -3.460048e-06  2.317025e-06
## StateMinnesota                   -5.255285e-05 -4.471538e-05 -3.687791e-05
## StateMississippi                  9.706533e-07  9.347470e-06  1.772429e-05
## StateMissouri                    -3.669987e-06  2.742331e-06  9.154649e-06
## StateMontana                     -5.313471e-05 -4.400468e-05 -3.487465e-05
## StateNebraska                    -3.217980e-05 -2.519839e-05 -1.821698e-05
## StateNevada                       1.405321e-05  2.224755e-05  3.044190e-05
## StateNew Hampshire                8.767847e-06  1.920309e-05  2.963832e-05
## StateNew Jersey                  -1.857314e-05 -9.100416e-06  3.723078e-07
## StateNew Mexico                   3.924470e-05  4.971824e-05  6.019177e-05
## StateNew York                    -1.782060e-05 -1.123309e-05 -4.645575e-06
## StateNorth Carolina               2.615187e-07  6.031550e-06  1.180158e-05
## StateNorth Dakota                -4.091613e-05 -3.190138e-05 -2.288664e-05
## StateOhio                         1.081251e-05  2.431685e-05  3.782118e-05
## StateOklahoma                     3.170529e-05  3.991344e-05  4.812160e-05
## StateOregon                      -3.257634e-05 -2.465486e-05 -1.673338e-05
## StatePennsylvania                 2.001744e-05  2.897951e-05  3.794158e-05
## StateRhode Island                 2.006083e-05  3.009142e-05  4.012200e-05
## StateSouth Carolina               2.383466e-05  3.160438e-05  3.937411e-05
## StateSouth Dakota                -2.884540e-05 -1.974829e-05 -1.065118e-05
## StateTennessee                    2.743183e-05  3.461431e-05  4.179679e-05
## StateTexas                       -2.637065e-05 -1.812418e-05 -9.877717e-06
## StateUtah                        -7.773335e-06 -8.578891e-07  6.057557e-06
## StateVermont                     -2.224538e-05 -1.439544e-05 -6.545498e-06
## StateVirginia                    -1.826035e-05 -1.258611e-05 -6.911877e-06
## StateWashington                  -1.623379e-05 -8.077755e-06  7.827891e-08
## StateWest Virginia                8.395092e-05  1.013932e-04  1.188355e-04
## StateWisconsin                   -1.612556e-05 -9.903718e-06 -3.681872e-06
## StateWyoming                     -2.239013e-06  4.817337e-06  1.187369e-05
## factor(Time_Period_ID)2          -9.597072e-06 -1.225815e-06  7.145441e-06
## factor(Time_Period_ID)3          -9.034921e-06 -7.059669e-07  7.622988e-06
## factor(Time_Period_ID)4          -8.615946e-06 -2.624190e-07  8.091108e-06
## factor(Time_Period_ID)5          -4.506297e-06  3.820036e-06  1.214637e-05
## factor(Time_Period_ID)6          -5.223238e-06  3.188753e-06  1.160074e-05
## factor(Time_Period_ID)7          -9.211372e-07  7.371229e-06  1.566360e-05
## factor(Time_Period_ID)8          -2.188981e-06  6.092335e-06  1.437365e-05
## factor(Time_Period_ID)9           1.018667e-07  8.252087e-06  1.640231e-05
## factor(Time_Period_ID)10         -1.638393e-06  6.567047e-06  1.477249e-05
## factor(Time_Period_ID)11          1.794641e-06  9.902275e-06  1.800991e-05
## factor(Time_Period_ID)12          7.328195e-07  9.748255e-06  1.876369e-05
## factor(Time_Period_ID)13          8.436350e-06  1.669515e-05  2.495395e-05
## factor(Time_Period_ID)14          1.005424e-05  1.854409e-05  2.703394e-05
## factor(Time_Period_ID)15          1.006564e-05  1.881056e-05  2.755549e-05
## factor(Time_Period_ID)16          1.031699e-05  1.899209e-05  2.766720e-05
## factor(Time_Period_ID)17          1.313487e-05  2.224645e-05  3.135803e-05
## factor(Time_Period_ID)18          1.056200e-05  1.950250e-05  2.844301e-05
## factor(Time_Period_ID)19          8.924215e-06  1.944967e-05  2.997513e-05
## factor(Time_Period_ID)20          7.440136e-06  1.734689e-05  2.725364e-05
## factor(Time_Period_ID)21          9.955337e-06  1.962960e-05  2.930387e-05
## factor(Time_Period_ID)22          6.878352e-06  1.699581e-05  2.711326e-05
## factor(Time_Period_ID)23          1.412365e-05  2.440944e-05  3.469523e-05
## factor(Time_Period_ID)24          1.217110e-05  2.277040e-05  3.336970e-05
## factor(Time_Period_ID)25          1.141998e-05  2.236039e-05  3.330081e-05
## factor(Time_Period_ID)26          9.762115e-06  2.074361e-05  3.172510e-05
## factor(Time_Period_ID)27          1.504140e-05  2.614184e-05  3.724228e-05
## factor(Time_Period_ID)28          1.193650e-05  2.343302e-05  3.492953e-05
## factor(Time_Period_ID)29          1.005025e-05  2.231965e-05  3.458905e-05
## factor(Time_Period_ID)30          1.004200e-05  2.271297e-05  3.538394e-05
## factor(Time_Period_ID)31          1.626465e-05  2.928890e-05  4.231315e-05
## factor(Time_Period_ID)32          1.612087e-05  2.948974e-05  4.285861e-05
## factor(Time_Period_ID)33          2.854000e-05  4.276776e-05  5.699551e-05
## factor(Time_Period_ID)34          3.038392e-05  4.538755e-05  6.039118e-05
## factor(Time_Period_ID)35          3.495050e-05  5.177306e-05  6.859562e-05
## factor(Time_Period_ID)36          3.310792e-05  4.976202e-05  6.641612e-05
## factor(Time_Period_ID)37          2.862394e-05  4.493881e-05  6.125369e-05
## factor(Time_Period_ID)38          2.477892e-05  4.171212e-05  5.864532e-05
## factor(Time_Period_ID)39          2.419129e-05  4.081074e-05  5.743019e-05
## factor(Time_Period_ID)40          3.164309e-05  4.924131e-05  6.683954e-05
## Naloxone_Pharmacy_Yes_Redefined  -7.581728e-06 -1.606767e-06  4.368193e-06
## Naloxone_Pharmacy_No_Redefined   -7.127586e-06 -2.293341e-06  2.540904e-06
## Medical_Marijuana_Redefined       1.275663e-05  1.771347e-05  2.267031e-05
## Recreational_Marijuana_Redefined -2.935318e-05 -2.062864e-05 -1.190411e-05
## GSL_Redefined                     3.312642e-06  7.828262e-06  1.234388e-05
## PDMP_Redefined                   -1.969320e-05 -1.628279e-05 -1.287237e-05
## Medicaid_Expansion_Redefined      9.533622e-06  1.417017e-05  1.880671e-05
## neg_2_pd                         -6.274166e-06 -6.703184e-07  4.933529e-06
## neg_3_pd                         -7.000043e-06 -1.008170e-06  4.983703e-06
## neg_4_pd                         -1.086181e-05 -4.527959e-06  1.805890e-06
## neg_5_pd                         -1.308077e-05 -7.416487e-06 -1.752199e-06
## neg_6_pd                         -1.450445e-05 -8.528134e-06 -2.551819e-06
## neg_7_pd                         -1.954347e-05 -1.274767e-05 -5.951873e-06
## neg_8_pd                         -2.430201e-05 -1.567091e-05 -7.039804e-06
## neg_9_pd                         -2.003909e-05 -1.310695e-05 -6.174822e-06
## neg_10_pd                        -2.177931e-05 -1.457926e-05 -7.379218e-06
## neg_11_pd                        -2.248824e-05 -1.526717e-05 -8.046107e-06
## neg_12_pd                        -2.156156e-05 -1.346421e-05 -5.366868e-06
## neg_13_pd                        -2.528649e-05 -1.743717e-05 -9.587852e-06
## neg_14_pd                        -2.854592e-05 -1.934006e-05 -1.013419e-05
## neg_15_pd                        -3.495990e-05 -2.438819e-05 -1.381648e-05
## neg_16_pd                        -3.473324e-05 -2.572456e-05 -1.671589e-05
## neg_17_pd                        -3.728714e-05 -2.762348e-05 -1.795982e-05
## neg_18_pd                        -3.984804e-05 -2.992887e-05 -2.000971e-05
## neg_19_pd                        -4.213891e-05 -3.146036e-05 -2.078180e-05
## neg_20_pd                        -4.688289e-05 -3.532104e-05 -2.375919e-05
## neg_21_pd                        -4.878762e-05 -3.583009e-05 -2.287256e-05
## neg_22_pd                        -5.289732e-05 -3.694092e-05 -2.098452e-05
## neg_23_pd                        -4.978031e-05 -3.407397e-05 -1.836763e-05
## neg_24_pd                        -5.637912e-05 -3.828529e-05 -2.019147e-05
## neg_25_pd                        -5.742895e-05 -3.707766e-05 -1.672636e-05
## neg_26_pd                        -5.904283e-05 -3.562540e-05 -1.220798e-05
## neg_27_pd                        -5.328433e-05 -3.538294e-05 -1.748154e-05
## neg_28_pd                        -5.329725e-05 -3.613286e-05 -1.896847e-05
## neg_29_pd                        -4.903661e-05 -3.344293e-05 -1.784926e-05
## neg_30_pd                        -5.296250e-05 -3.654051e-05 -2.011851e-05
## neg_31_pd                        -5.623422e-05 -3.942031e-05 -2.260640e-05
## neg_32_pd                        -6.287718e-05 -4.412086e-05 -2.536454e-05
## neg_33_pd                        -6.760776e-05 -3.872554e-05 -9.843312e-06
## pos_0_pd                         -5.320048e-06  5.034363e-07  6.326921e-06
## pos_1_pd                         -7.284032e-06 -5.833719e-07  6.117288e-06
## pos_2_pd                         -3.260502e-06  3.350705e-06  9.961911e-06
## pos_3_pd                         -4.355226e-06  2.685961e-06  9.727149e-06
## pos_4_pd                         -3.656354e-06  4.165419e-06  1.198719e-05
## pos_5_pd                         -4.508676e-06  2.911528e-06  1.033173e-05
## pos_6_pd                         -3.001597e-06  5.521126e-06  1.404385e-05
## pos_7_pd                         -3.360018e-06  4.641613e-06  1.264325e-05
## pos_8_pd                         -4.432811e-06  4.601253e-06  1.363532e-05
## pos_9_pd                         -2.883241e-06  5.122046e-06  1.312733e-05
## pos_10_pd                        -2.563565e-06  5.692585e-06  1.394873e-05
## pos_11_pd                        -1.614462e-06  6.549633e-06  1.471373e-05
## pos_12_pd                         1.224820e-06  9.126041e-06  1.702726e-05
## pos_13_pd                        -2.597916e-06  6.685110e-06  1.596814e-05
## pos_14_pd                         1.014850e-06  9.568026e-06  1.812120e-05
## pos_15_pd                        -5.288352e-07  9.313612e-06  1.915606e-05
## pos_16_pd                        -2.928264e-07  9.564428e-06  1.942168e-05
## pos_17_pd                         1.945399e-06  1.344625e-05  2.494709e-05
## pos_18_pd                         5.903107e-06  1.668558e-05  2.746806e-05
## pos_19_pd                         7.727145e-06  1.766528e-05  2.760341e-05
## pos_20_pd                         7.746674e-06  1.843406e-05  2.912145e-05
## pos_21_pd                         7.427666e-06  1.837290e-05  2.931813e-05
## pos_22_pd                         7.904873e-06  1.931568e-05  3.072649e-05
## pos_23_pd                         6.230583e-06  1.877273e-05  3.131487e-05
## pos_24_pd                         5.839190e-07  1.212190e-05  2.365987e-05
## pos_25_pd                         3.418988e-06  1.598852e-05  2.855806e-05
## pos_26_pd                         5.776694e-06  1.866037e-05  3.154406e-05
## pos_27_pd                         3.088993e-06  1.652909e-05  2.996919e-05
## pos_28_pd                         5.913150e-06  2.005808e-05  3.420302e-05
## pos_29_pd                         4.555448e-06  2.106577e-05  3.757608e-05
## pos_30_pd                         9.999101e-06  2.694735e-05  4.389561e-05
## pos_31_pd                         1.765453e-05  3.953294e-05  6.141135e-05
## pos_32_pd                         1.231996e-05  4.049465e-05  6.866934e-05
## pos_33_pd                         1.478374e-05  4.292117e-05  7.105860e-05
## pos_34_pd                         1.416440e-05  4.818733e-05  8.221026e-05
## pos_35_pd                         1.221796e-05  3.797534e-05  6.373273e-05
## pos_36_pd                         1.196206e-05  3.246222e-05  5.296239e-05
## pos_37_pd                         2.456961e-05  5.077491e-05  7.698020e-05
## pos_38_pd                         1.098930e-05  5.047506e-05  8.996082e-05
## pos_39_pd                        -8.116398e-06  4.850436e-05  1.051251e-04
##                                       sd_coef
## (Intercept)                      5.042481e-06
## StateAlaska                      5.388790e-06
## StateArizona                     3.842818e-06
## StateArkansas                    3.689620e-06
## StateCalifornia                  4.924741e-06
## StateColorado                    4.157395e-06
## StateConnecticut                 4.388057e-06
## StateDelaware                    7.470584e-06
## StateFlorida                     3.837075e-06
## StateGeorgia                     4.194913e-06
## StateHawaii                      3.856525e-06
## StateIdaho                       4.332764e-06
## StateIllinois                    3.875664e-06
## StateIndiana                     2.883979e-06
## StateIowa                        3.299102e-06
## StateKansas                      2.898539e-06
## StateKentucky                    3.902659e-06
## StateLouisiana                   3.532555e-06
## StateMaine                       5.454253e-06
## StateMaryland                    4.120863e-06
## StateMassachusetts               5.195930e-06
## StateMichigan                    2.947486e-06
## StateMinnesota                   3.998708e-06
## StateMississippi                 4.273886e-06
## StateMissouri                    3.271591e-06
## StateMontana                     4.658177e-06
## StateNebraska                    3.561944e-06
## StateNevada                      4.180787e-06
## StateNew Hampshire               5.324101e-06
## StateNew Jersey                  4.833022e-06
## StateNew Mexico                  5.343640e-06
## StateNew York                    3.360975e-06
## StateNorth Carolina              2.943894e-06
## StateNorth Dakota                4.599358e-06
## StateOhio                        6.889967e-06
## StateOklahoma                    4.187833e-06
## StateOregon                      4.041571e-06
## StatePennsylvania                4.572486e-06
## StateRhode Island                5.117645e-06
## StateSouth Carolina              3.964145e-06
## StateSouth Dakota                4.641382e-06
## StateTennessee                   3.664531e-06
## StateTexas                       4.207381e-06
## StateUtah                        3.528289e-06
## StateVermont                     4.005073e-06
## StateVirginia                    2.895018e-06
## StateWashington                  4.161242e-06
## StateWest Virginia               8.899132e-06
## StateWisconsin                   3.174411e-06
## StateWyoming                     3.600178e-06
## factor(Time_Period_ID)2          4.271049e-06
## factor(Time_Period_ID)3          4.249467e-06
## factor(Time_Period_ID)4          4.262003e-06
## factor(Time_Period_ID)5          4.248129e-06
## factor(Time_Period_ID)6          4.291832e-06
## factor(Time_Period_ID)7          4.230799e-06
## factor(Time_Period_ID)8          4.225161e-06
## factor(Time_Period_ID)9          4.158276e-06
## factor(Time_Period_ID)10         4.186449e-06
## factor(Time_Period_ID)11         4.136548e-06
## factor(Time_Period_ID)12         4.599712e-06
## factor(Time_Period_ID)13         4.213673e-06
## factor(Time_Period_ID)14         4.331555e-06
## factor(Time_Period_ID)15         4.461697e-06
## factor(Time_Period_ID)16         4.426075e-06
## factor(Time_Period_ID)17         4.648766e-06
## factor(Time_Period_ID)18         4.561482e-06
## factor(Time_Period_ID)19         5.370131e-06
## factor(Time_Period_ID)20         5.054466e-06
## factor(Time_Period_ID)21         4.935849e-06
## factor(Time_Period_ID)22         5.161966e-06
## factor(Time_Period_ID)23         5.247851e-06
## factor(Time_Period_ID)24         5.407808e-06
## factor(Time_Period_ID)25         5.581842e-06
## factor(Time_Period_ID)26         5.602802e-06
## factor(Time_Period_ID)27         5.663489e-06
## factor(Time_Period_ID)28         5.865569e-06
## factor(Time_Period_ID)29         6.259897e-06
## factor(Time_Period_ID)30         6.464780e-06
## factor(Time_Period_ID)31         6.645023e-06
## factor(Time_Period_ID)32         6.820853e-06
## factor(Time_Period_ID)33         7.259057e-06
## factor(Time_Period_ID)34         7.654915e-06
## factor(Time_Period_ID)35         8.582940e-06
## factor(Time_Period_ID)36         8.496990e-06
## factor(Time_Period_ID)37         8.323916e-06
## factor(Time_Period_ID)38         8.639389e-06
## factor(Time_Period_ID)39         8.479311e-06
## factor(Time_Period_ID)40         8.978687e-06
## Naloxone_Pharmacy_Yes_Redefined  3.048449e-06
## Naloxone_Pharmacy_No_Redefined   2.466452e-06
## Medical_Marijuana_Redefined      2.528999e-06
## Recreational_Marijuana_Redefined 4.451295e-06
## GSL_Redefined                    2.303888e-06
## PDMP_Redefined                   1.740010e-06
## Medicaid_Expansion_Redefined     2.365584e-06
## neg_2_pd                         2.859106e-06
## neg_3_pd                         3.057078e-06
## neg_4_pd                         3.231555e-06
## neg_5_pd                         2.889942e-06
## neg_6_pd                         3.049140e-06
## neg_7_pd                         3.467244e-06
## neg_8_pd                         4.403624e-06
## neg_9_pd                         3.536802e-06
## neg_10_pd                        3.673492e-06
## neg_11_pd                        3.684217e-06
## neg_12_pd                        4.131299e-06
## neg_13_pd                        4.004753e-06
## neg_14_pd                        4.696871e-06
## neg_15_pd                        5.393730e-06
## neg_16_pd                        4.596263e-06
## neg_17_pd                        4.930439e-06
## neg_18_pd                        5.060800e-06
## neg_19_pd                        5.448243e-06
## neg_20_pd                        5.898902e-06
## neg_21_pd                        6.610985e-06
## neg_22_pd                        8.141021e-06
## neg_23_pd                        8.013439e-06
## neg_24_pd                        9.231543e-06
## neg_25_pd                        1.038331e-05
## neg_26_pd                        1.194766e-05
## neg_27_pd                        9.133365e-06
## neg_28_pd                        8.757342e-06
## neg_29_pd                        7.955958e-06
## neg_30_pd                        8.378570e-06
## neg_31_pd                        8.578524e-06
## neg_32_pd                        9.569551e-06
## neg_33_pd                        1.473583e-05
## pos_0_pd                         2.971165e-06
## pos_1_pd                         3.418704e-06
## pos_2_pd                         3.373065e-06
## pos_3_pd                         3.592443e-06
## pos_4_pd                         3.990701e-06
## pos_5_pd                         3.785818e-06
## pos_6_pd                         4.348328e-06
## pos_7_pd                         4.082465e-06
## pos_8_pd                         4.609216e-06
## pos_9_pd                         4.084330e-06
## pos_10_pd                        4.212321e-06
## pos_11_pd                        4.165355e-06
## pos_12_pd                        4.031235e-06
## pos_13_pd                        4.736238e-06
## pos_14_pd                        4.363865e-06
## pos_15_pd                        5.021657e-06
## pos_16_pd                        5.029211e-06
## pos_17_pd                        5.867779e-06
## pos_18_pd                        5.501263e-06
## pos_19_pd                        5.070477e-06
## pos_20_pd                        5.452749e-06
## pos_21_pd                        5.584302e-06
## pos_22_pd                        5.821842e-06
## pos_23_pd                        6.399054e-06
## pos_24_pd                        5.886723e-06
## pos_25_pd                        6.413029e-06
## pos_26_pd                        6.573306e-06
## pos_27_pd                        6.857193e-06
## pos_28_pd                        7.216803e-06
## pos_29_pd                        8.423631e-06
## pos_30_pd                        8.647068e-06
## pos_31_pd                        1.116245e-05
## pos_32_pd                        1.437484e-05
## pos_33_pd                        1.435583e-05
## pos_34_pd                        1.735864e-05
## pos_35_pd                        1.314152e-05
## pos_36_pd                        1.045927e-05
## pos_37_pd                        1.337005e-05
## pos_38_pd                        2.014580e-05
## pos_39_pd                        2.888814e-05
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")

6.2.3 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_fixed_time <- sensitivity_anlys_event_study_sd_and_ci_fixed_time %>%
  mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_fixed_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study_fixed_time, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

6.3 Analysis With Only Periods After Treatment

formula_post_tx_fixed_time <- formula(paste("prop_dead~ State +
                                           factor(Time_Period_ID)  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_fixed_time<-lm(formula_post_tx_fixed_time,
                                         data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_fixed_time)
## 
## Call:
## lm(formula = formula_post_tx_fixed_time, data = sensitivity_anlys_event_study_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.034e-04 -1.161e-05  8.900e-08  1.119e-05  1.324e-04 
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       2.674e-05  4.473e-06   5.977 2.71e-09 ***
## StateAlaska                      -3.115e-06  5.329e-06  -0.584 0.558967    
## StateArizona                      9.139e-06  4.846e-06   1.886 0.059474 .  
## StateArkansas                    -2.964e-05  4.771e-06  -6.212 6.42e-10 ***
## StateCalifornia                  -1.898e-05  5.387e-06  -3.523 0.000438 ***
## StateColorado                    -8.754e-06  5.240e-06  -1.671 0.094980 .  
## StateConnecticut                  1.246e-05  5.015e-06   2.484 0.013061 *  
## StateDelaware                     1.719e-05  4.924e-06   3.491 0.000493 ***
## StateFlorida                      1.769e-05  4.984e-06   3.549 0.000397 ***
## StateGeorgia                     -4.013e-06  5.096e-06  -0.787 0.431123    
## StateHawaii                      -3.318e-05  5.267e-06  -6.300 3.71e-10 ***
## StateIdaho                       -9.590e-06  4.818e-06  -1.991 0.046677 *  
## StateIllinois                     5.085e-06  4.931e-06   1.031 0.302625    
## StateIndiana                      1.157e-05  4.726e-06   2.449 0.014411 *  
## StateIowa                        -2.884e-05  4.785e-06  -6.028 1.99e-09 ***
## StateKansas                      -1.454e-05  4.695e-06  -3.097 0.001983 ** 
## StateKentucky                     5.662e-05  4.775e-06  11.857  < 2e-16 ***
## StateLouisiana                    2.363e-05  4.755e-06   4.968 7.38e-07 ***
## StateMaine                        2.812e-06  5.225e-06   0.538 0.590523    
## StateMaryland                    -5.118e-05  4.925e-06 -10.393  < 2e-16 ***
## StateMassachusetts                2.002e-05  4.773e-06   4.195 2.86e-05 ***
## StateMichigan                     2.333e-06  4.875e-06   0.479 0.632270    
## StateMinnesota                   -4.357e-05  4.928e-06  -8.841  < 2e-16 ***
## StateMississippi                 -8.831e-06  4.760e-06  -1.855 0.063751 .  
## StateMissouri                     1.041e-05  4.869e-06   2.137 0.032709 *  
## StateMontana                     -3.371e-05  5.030e-06  -6.702 2.71e-11 ***
## StateNebraska                    -3.919e-05  4.818e-06  -8.135 7.44e-16 ***
## StateNevada                       2.739e-05  5.087e-06   5.385 8.16e-08 ***
## StateNew Hampshire                1.380e-05  4.776e-06   2.889 0.003911 ** 
## StateNew Jersey                   5.827e-06  4.929e-06   1.182 0.237323    
## StateNew Mexico                   4.307e-05  5.142e-06   8.376  < 2e-16 ***
## StateNew York                    -1.034e-05  4.846e-06  -2.134 0.032946 *  
## StateNorth Carolina               1.400e-05  4.712e-06   2.971 0.003008 ** 
## StateNorth Dakota                -4.604e-05  4.771e-06  -9.649  < 2e-16 ***
## StateOhio                         4.561e-05  5.114e-06   8.919  < 2e-16 ***
## StateOklahoma                     3.044e-05  4.742e-06   6.418 1.74e-10 ***
## StateOregon                      -3.018e-05  5.200e-06  -5.804 7.60e-09 ***
## StatePennsylvania                 4.731e-05  4.997e-06   9.469  < 2e-16 ***
## StateRhode Island                 1.209e-05  4.973e-06   2.430 0.015181 *  
## StateSouth Carolina               9.715e-06  4.803e-06   2.023 0.043236 *  
## StateSouth Dakota                -4.267e-05  4.846e-06  -8.806  < 2e-16 ***
## StateTennessee                    3.440e-05  4.665e-06   7.374 2.48e-13 ***
## StateTexas                       -1.227e-06  4.957e-06  -0.248 0.804541    
## StateUtah                         5.357e-06  4.721e-06   1.135 0.256680    
## StateVermont                     -1.951e-05  4.927e-06  -3.960 7.78e-05 ***
## StateVirginia                    -7.187e-07  4.778e-06  -0.150 0.880450    
## StateWashington                  -1.075e-05  5.268e-06  -2.040 0.041448 *  
## StateWest Virginia                8.687e-05  4.791e-06  18.134  < 2e-16 ***
## StateWisconsin                    1.114e-06  4.764e-06   0.234 0.815148    
## StateWyoming                      3.067e-07  4.697e-06   0.065 0.947943    
## factor(Time_Period_ID)2          -8.148e-07  4.170e-06  -0.195 0.845101    
## factor(Time_Period_ID)3           1.392e-06  4.169e-06   0.334 0.738528    
## factor(Time_Period_ID)4           3.217e-06  4.173e-06   0.771 0.440776    
## factor(Time_Period_ID)5           8.682e-06  4.177e-06   2.078 0.037805 *  
## factor(Time_Period_ID)6           9.464e-06  4.179e-06   2.265 0.023651 *  
## factor(Time_Period_ID)7           1.492e-05  4.186e-06   3.563 0.000375 ***
## factor(Time_Period_ID)8           1.474e-05  4.189e-06   3.519 0.000443 ***
## factor(Time_Period_ID)9           1.788e-05  4.197e-06   4.260 2.14e-05 ***
## factor(Time_Period_ID)10          1.752e-05  4.211e-06   4.161 3.31e-05 ***
## factor(Time_Period_ID)11          2.213e-05  4.221e-06   5.243 1.76e-07 ***
## factor(Time_Period_ID)12          2.307e-05  4.246e-06   5.434 6.25e-08 ***
## factor(Time_Period_ID)13          3.140e-05  4.267e-06   7.358 2.78e-13 ***
## factor(Time_Period_ID)14          3.497e-05  4.291e-06   8.149 6.64e-16 ***
## factor(Time_Period_ID)15          3.682e-05  4.298e-06   8.567  < 2e-16 ***
## factor(Time_Period_ID)16          3.789e-05  4.330e-06   8.751  < 2e-16 ***
## factor(Time_Period_ID)17          4.262e-05  4.374e-06   9.744  < 2e-16 ***
## factor(Time_Period_ID)18          4.134e-05  4.406e-06   9.382  < 2e-16 ***
## factor(Time_Period_ID)19          4.231e-05  4.431e-06   9.548  < 2e-16 ***
## factor(Time_Period_ID)20          4.172e-05  4.478e-06   9.318  < 2e-16 ***
## factor(Time_Period_ID)21          4.550e-05  4.524e-06  10.057  < 2e-16 ***
## factor(Time_Period_ID)22          4.392e-05  4.569e-06   9.613  < 2e-16 ***
## factor(Time_Period_ID)23          5.273e-05  4.613e-06  11.432  < 2e-16 ***
## factor(Time_Period_ID)24          5.216e-05  4.696e-06  11.108  < 2e-16 ***
## factor(Time_Period_ID)25          5.286e-05  4.731e-06  11.173  < 2e-16 ***
## factor(Time_Period_ID)26          5.255e-05  4.790e-06  10.971  < 2e-16 ***
## factor(Time_Period_ID)27          5.909e-05  4.865e-06  12.146  < 2e-16 ***
## factor(Time_Period_ID)28          5.765e-05  4.935e-06  11.682  < 2e-16 ***
## factor(Time_Period_ID)29          5.851e-05  5.027e-06  11.639  < 2e-16 ***
## factor(Time_Period_ID)30          6.016e-05  5.140e-06  11.705  < 2e-16 ***
## factor(Time_Period_ID)31          6.808e-05  5.219e-06  13.044  < 2e-16 ***
## factor(Time_Period_ID)32          6.941e-05  5.442e-06  12.756  < 2e-16 ***
## factor(Time_Period_ID)33          8.387e-05  5.595e-06  14.990  < 2e-16 ***
## factor(Time_Period_ID)34          8.760e-05  5.814e-06  15.066  < 2e-16 ***
## factor(Time_Period_ID)35          9.503e-05  5.915e-06  16.067  < 2e-16 ***
## factor(Time_Period_ID)36          9.429e-05  6.067e-06  15.541  < 2e-16 ***
## factor(Time_Period_ID)37          9.078e-05  6.123e-06  14.825  < 2e-16 ***
## factor(Time_Period_ID)38          8.881e-05  6.218e-06  14.282  < 2e-16 ***
## factor(Time_Period_ID)39          8.921e-05  6.318e-06  14.119  < 2e-16 ***
## factor(Time_Period_ID)40          9.890e-05  6.370e-06  15.527  < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined  -7.926e-07  3.118e-06  -0.254 0.799383    
## Naloxone_Pharmacy_No_Redefined   -1.692e-06  2.652e-06  -0.638 0.523627    
## Medical_Marijuana_Redefined       1.924e-05  2.101e-06   9.158  < 2e-16 ***
## Recreational_Marijuana_Redefined -1.904e-05  3.170e-06  -6.005 2.29e-09 ***
## GSL_Redefined                     7.397e-06  2.211e-06   3.346 0.000837 ***
## PDMP_Redefined                   -1.482e-05  1.751e-06  -8.466  < 2e-16 ***
## Medicaid_Expansion_Redefined      1.257e-05  2.168e-06   5.795 8.01e-09 ***
## pos_0_pd                          1.616e-06  3.289e-06   0.491 0.623357    
## pos_1_pd                         -7.711e-07  3.319e-06  -0.232 0.816302    
## pos_2_pd                          1.818e-06  3.348e-06   0.543 0.587112    
## pos_3_pd                         -1.410e-07  3.388e-06  -0.042 0.966821    
## pos_4_pd                          3.618e-08  3.429e-06   0.011 0.991583    
## pos_5_pd                         -2.445e-06  3.481e-06  -0.702 0.482636    
## pos_6_pd                         -1.077e-06  3.548e-06  -0.304 0.761501    
## pos_7_pd                         -3.237e-06  3.612e-06  -0.896 0.370283    
## pos_8_pd                         -4.663e-06  3.724e-06  -1.252 0.210668    
## pos_9_pd                         -5.499e-06  3.804e-06  -1.446 0.148449    
## pos_10_pd                        -6.205e-06  3.856e-06  -1.609 0.107696    
## pos_11_pd                        -6.792e-06  3.942e-06  -1.723 0.085025 .  
## pos_12_pd                        -5.603e-06  4.023e-06  -1.393 0.163892    
## pos_13_pd                        -9.318e-06  4.078e-06  -2.285 0.022422 *  
## pos_14_pd                        -7.893e-06  4.235e-06  -1.864 0.062510 .  
## pos_15_pd                        -9.490e-06  4.340e-06  -2.186 0.028914 *  
## pos_16_pd                        -1.053e-05  4.405e-06  -2.391 0.016921 *  
## pos_17_pd                        -8.141e-06  4.575e-06  -1.779 0.075368 .  
## pos_18_pd                        -6.191e-06  4.688e-06  -1.321 0.186805    
## pos_19_pd                        -6.413e-06  4.752e-06  -1.350 0.177251    
## pos_20_pd                        -7.121e-06  4.956e-06  -1.437 0.150990    
## pos_21_pd                        -8.407e-06  5.170e-06  -1.626 0.104111    
## pos_22_pd                        -8.850e-06  5.298e-06  -1.670 0.095009 .  
## pos_23_pd                        -1.071e-05  5.433e-06  -1.972 0.048749 *  
## pos_24_pd                        -1.860e-05  5.800e-06  -3.207 0.001364 ** 
## pos_25_pd                        -1.602e-05  6.141e-06  -2.608 0.009173 ** 
## pos_26_pd                        -1.466e-05  6.205e-06  -2.363 0.018217 *  
## pos_27_pd                        -1.828e-05  6.278e-06  -2.911 0.003645 ** 
## pos_28_pd                        -1.595e-05  6.360e-06  -2.508 0.012229 *  
## pos_29_pd                        -1.608e-05  6.936e-06  -2.319 0.020517 *  
## pos_30_pd                        -1.151e-05  7.160e-06  -1.608 0.108059    
## pos_31_pd                        -3.809e-07  7.410e-06  -0.051 0.959009    
## pos_32_pd                        -8.162e-07  8.171e-06  -0.100 0.920448    
## pos_33_pd                         6.965e-08  8.558e-06   0.008 0.993507    
## pos_34_pd                         4.066e-06  8.628e-06   0.471 0.637521    
## pos_35_pd                        -7.522e-06  1.006e-05  -0.748 0.454706    
## pos_36_pd                        -1.433e-05  1.012e-05  -1.416 0.156930    
## pos_37_pd                         2.566e-06  1.197e-05   0.214 0.830242    
## pos_38_pd                         1.193e-06  1.614e-05   0.074 0.941082    
## pos_39_pd                        -2.044e-06  1.619e-05  -0.126 0.899550    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.083e-05 on 1864 degrees of freedom
## Multiple R-squared:  0.806,  Adjusted R-squared:  0.7919 
## F-statistic: 57.35 on 135 and 1864 DF,  p-value: < 2.2e-16

6.3.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_fixed_time <- model.matrix(sensitivity_anlys_post_tx_model_fixed_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_fixed_time <- coef(sensitivity_anlys_post_tx_model_fixed_time)

sensitivity_anlys_post_tx_sd_and_ci_fixed_time <- compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_fixed_time), 
                                                         sensitivity_anlys_event_study_data$prop_dead,
                                                         coefficient_values_sensitivity_anlys_post_tx_fixed_time, 
                                                         p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_fixed_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_fixed_time
##                                        lb_coef   coef_values       ub_coef
## (Intercept)                       1.926109e-05  2.673763e-05  3.421417e-05
## StateAlaska                      -1.178898e-05 -3.114563e-06  5.559854e-06
## StateArizona                      2.425635e-06  9.138522e-06  1.585141e-05
## StateArkansas                    -3.653442e-05 -2.963777e-05 -2.274112e-05
## StateCalifornia                  -2.811939e-05 -1.897606e-05 -9.832728e-06
## StateColorado                    -1.613416e-05 -8.753872e-06 -1.373581e-06
## StateConnecticut                  3.964301e-06  1.246077e-05  2.095723e-05
## StateDelaware                     4.690111e-06  1.718974e-05  2.968937e-05
## StateFlorida                      1.149270e-05  1.768587e-05  2.387903e-05
## StateGeorgia                     -1.070454e-05 -4.012762e-06  2.679017e-06
## StateHawaii                      -4.185938e-05 -3.318200e-05 -2.450463e-05
## StateIdaho                       -1.600585e-05 -9.590245e-06 -3.174641e-06
## StateIllinois                    -1.944101e-06  5.084563e-06  1.211323e-05
## StateIndiana                      5.917598e-06  1.157477e-05  1.723194e-05
## StateIowa                        -3.454564e-05 -2.884364e-05 -2.314164e-05
## StateKansas                      -2.004813e-05 -1.453994e-05 -9.031744e-06
## StateKentucky                     4.880712e-05  5.661629e-05  6.442545e-05
## StateLouisiana                    1.737451e-05  2.362503e-05  2.987555e-05
## StateMaine                       -7.666751e-06  2.812057e-06  1.329087e-05
## StateMaryland                    -5.840156e-05 -5.118158e-05 -4.396159e-05
## StateMassachusetts                9.844275e-06  2.001927e-05  3.019427e-05
## StateMichigan                    -3.303553e-06  2.333077e-06  7.969707e-06
## StateMinnesota                   -5.127013e-05 -4.357057e-05 -3.587100e-05
## StateMississippi                 -1.547806e-05 -8.830505e-06 -2.182946e-06
## StateMissouri                     4.492074e-06  1.040698e-05  1.632189e-05
## StateMontana                     -4.263540e-05 -3.371207e-05 -2.478874e-05
## StateNebraska                    -4.528139e-05 -3.919208e-05 -3.310276e-05
## StateNevada                       1.931649e-05  2.739325e-05  3.547001e-05
## StateNew Hampshire                3.559226e-06  1.379773e-05  2.403624e-05
## StateNew Jersey                  -2.835253e-06  5.826605e-06  1.448846e-05
## StateNew Mexico                   3.303994e-05  4.306669e-05  5.309344e-05
## StateNew York                    -1.677034e-05 -1.034305e-05 -3.915748e-06
## StateNorth Carolina               8.637619e-06  1.399921e-05  1.936080e-05
## StateNorth Dakota                -5.415597e-05 -4.603673e-05 -3.791748e-05
## StateOhio                         3.281368e-05  4.560641e-05  5.839915e-05
## StateOklahoma                     2.253672e-05  3.043670e-05  3.833668e-05
## StateOregon                      -3.781999e-05 -3.017922e-05 -2.253845e-05
## StatePennsylvania                 3.914230e-05  4.731155e-05  5.548080e-05
## StateRhode Island                 2.624633e-06  1.208508e-05  2.154554e-05
## StateSouth Carolina               4.356663e-06  9.714901e-06  1.507314e-05
## StateSouth Dakota                -4.941627e-05 -4.267203e-05 -3.592779e-05
## StateTennessee                    2.734363e-05  3.440158e-05  4.145954e-05
## StateTexas                       -8.857649e-06 -1.226835e-06  6.403979e-06
## StateUtah                        -1.357718e-06  5.357010e-06  1.207174e-05
## StateVermont                     -2.724877e-05 -1.950978e-05 -1.177079e-05
## StateVirginia                    -5.815439e-06 -7.187361e-07  4.377967e-06
## StateWashington                  -1.875728e-05 -1.074987e-05 -2.742465e-06
## StateWest Virginia                6.929496e-05  8.687276e-05  1.044505e-04
## StateWisconsin                   -4.306579e-06  1.113949e-06  6.534478e-06
## StateWyoming                     -6.603642e-06  3.067285e-07  7.217099e-06
## factor(Time_Period_ID)2          -9.593816e-06 -8.147579e-07  7.964301e-06
## factor(Time_Period_ID)3          -7.152790e-06  1.391839e-06  9.936467e-06
## factor(Time_Period_ID)4          -5.341024e-06  3.217313e-06  1.177565e-05
## factor(Time_Period_ID)5           1.088454e-07  8.681776e-06  1.725471e-05
## factor(Time_Period_ID)6           1.152168e-06  9.464465e-06  1.777676e-05
## factor(Time_Period_ID)7           6.753696e-06  1.491742e-05  2.308114e-05
## factor(Time_Period_ID)8           6.602689e-06  1.474306e-05  2.288343e-05
## factor(Time_Period_ID)9           9.981193e-06  1.788163e-05  2.578208e-05
## factor(Time_Period_ID)10          9.570509e-06  1.752128e-05  2.547205e-05
## factor(Time_Period_ID)11          1.443397e-05  2.213123e-05  2.982850e-05
## factor(Time_Period_ID)12          1.449619e-05  2.307238e-05  3.164857e-05
## factor(Time_Period_ID)13          2.360748e-05  3.139618e-05  3.918488e-05
## factor(Time_Period_ID)14          2.712613e-05  3.496652e-05  4.280691e-05
## factor(Time_Period_ID)15          2.878928e-05  3.681815e-05  4.484703e-05
## factor(Time_Period_ID)16          3.000808e-05  3.789160e-05  4.577511e-05
## factor(Time_Period_ID)17          3.434205e-05  4.261661e-05  5.089117e-05
## factor(Time_Period_ID)18          3.341175e-05  4.134169e-05  4.927162e-05
## factor(Time_Period_ID)19          3.264751e-05  4.231038e-05  5.197325e-05
## factor(Time_Period_ID)20          3.295743e-05  4.172170e-05  5.048597e-05
## factor(Time_Period_ID)21          3.709225e-05  4.550190e-05  5.391155e-05
## factor(Time_Period_ID)22          3.522925e-05  4.391906e-05  5.260887e-05
## factor(Time_Period_ID)23          4.401627e-05  5.273306e-05  6.144984e-05
## factor(Time_Period_ID)24          4.311571e-05  5.216197e-05  6.120823e-05
## factor(Time_Period_ID)25          4.372822e-05  5.285816e-05  6.198810e-05
## factor(Time_Period_ID)26          4.343225e-05  5.254590e-05  6.165955e-05
## factor(Time_Period_ID)27          4.992913e-05  5.909109e-05  6.825305e-05
## factor(Time_Period_ID)28          4.832476e-05  5.764999e-05  6.697522e-05
## factor(Time_Period_ID)29          4.884542e-05  5.850712e-05  6.816882e-05
## factor(Time_Period_ID)30          5.001869e-05  6.016252e-05  7.030635e-05
## factor(Time_Period_ID)31          5.776697e-05  6.807854e-05  7.839011e-05
## factor(Time_Period_ID)32          5.855183e-05  6.941405e-05  8.027627e-05
## factor(Time_Period_ID)33          7.194099e-05  8.387416e-05  9.580733e-05
## factor(Time_Period_ID)34          7.459926e-05  8.759961e-05  1.006000e-04
## factor(Time_Period_ID)35          7.980179e-05  9.503294e-05  1.102641e-04
## factor(Time_Period_ID)36          7.990080e-05  9.429114e-05  1.086815e-04
## factor(Time_Period_ID)37          7.676103e-05  9.078293e-05  1.048048e-04
## factor(Time_Period_ID)38          7.385274e-05  8.880884e-05  1.037650e-04
## factor(Time_Period_ID)39          7.507232e-05  8.920826e-05  1.033442e-04
## factor(Time_Period_ID)40          8.314134e-05  9.890490e-05  1.146685e-04
## Naloxone_Pharmacy_Yes_Redefined  -6.763419e-06 -7.926449e-07  5.178129e-06
## Naloxone_Pharmacy_No_Redefined   -6.431447e-06 -1.691816e-06  3.047815e-06
## Medical_Marijuana_Redefined       1.427207e-05  1.923783e-05  2.420359e-05
## Recreational_Marijuana_Redefined -2.758248e-05 -1.903665e-05 -1.049082e-05
## GSL_Redefined                     2.918033e-06  7.396887e-06  1.187574e-05
## PDMP_Redefined                   -1.816936e-05 -1.482011e-05 -1.147086e-05
## Medicaid_Expansion_Redefined      8.025852e-06  1.256512e-05  1.710439e-05
## pos_0_pd                         -3.179500e-06  1.615661e-06  6.410822e-06
## pos_1_pd                         -6.564751e-06 -7.711315e-07  5.022488e-06
## pos_2_pd                         -3.972742e-06  1.818146e-06  7.609033e-06
## pos_3_pd                         -6.332154e-06 -1.409543e-07  6.050246e-06
## pos_4_pd                         -6.849249e-06  3.617501e-08  6.921599e-06
## pos_5_pd                         -9.055662e-06 -2.444664e-06  4.166333e-06
## pos_6_pd                         -8.678598e-06 -1.077151e-06  6.524296e-06
## pos_7_pd                         -1.039943e-05 -3.236978e-06  3.925474e-06
## pos_8_pd                         -1.275496e-05 -4.662586e-06  3.429786e-06
## pos_9_pd                         -1.263255e-05 -5.499503e-06  1.633548e-06
## pos_10_pd                        -1.366773e-05 -6.205140e-06  1.257454e-06
## pos_11_pd                        -1.401242e-05 -6.791952e-06  4.285199e-07
## pos_12_pd                        -1.250777e-05 -5.603034e-06  1.301704e-06
## pos_13_pd                        -1.755142e-05 -9.317522e-06 -1.083621e-06
## pos_14_pd                        -1.542968e-05 -7.893126e-06 -3.565699e-07
## pos_15_pd                        -1.821065e-05 -9.489572e-06 -7.684925e-07
## pos_16_pd                        -1.928977e-05 -1.053090e-05 -1.772033e-06
## pos_17_pd                        -1.873585e-05 -8.140657e-06  2.454532e-06
## pos_18_pd                        -1.581595e-05 -6.191031e-06  3.433888e-06
## pos_19_pd                        -1.501200e-05 -6.413490e-06  2.185018e-06
## pos_20_pd                        -1.634603e-05 -7.120668e-06  2.104691e-06
## pos_21_pd                        -1.782887e-05 -8.406866e-06  1.015139e-06
## pos_22_pd                        -1.871128e-05 -8.850347e-06  1.010582e-06
## pos_23_pd                        -2.188898e-05 -1.071458e-05  4.598232e-07
## pos_24_pd                        -2.856448e-05 -1.860038e-05 -8.636280e-06
## pos_25_pd                        -2.700627e-05 -1.601623e-05 -5.026179e-06
## pos_26_pd                        -2.592827e-05 -1.466370e-05 -3.399140e-06
## pos_27_pd                        -2.977251e-05 -1.827661e-05 -6.780711e-06
## pos_28_pd                        -2.843133e-05 -1.594954e-05 -3.467745e-06
## pos_29_pd                        -3.121158e-05 -1.608384e-05 -9.560911e-07
## pos_30_pd                        -2.689457e-05 -1.151111e-05  3.872346e-06
## pos_31_pd                        -2.099949e-05 -3.808817e-07  2.023773e-05
## pos_32_pd                        -2.786027e-05 -8.161694e-07  2.622793e-05
## pos_33_pd                        -2.668938e-05  6.965456e-08  2.682869e-05
## pos_34_pd                        -2.901486e-05  4.065885e-06  3.714663e-05
## pos_35_pd                        -3.178977e-05 -7.521940e-06  1.674589e-05
## pos_36_pd                        -3.298920e-05 -1.432901e-05  4.331174e-06
## pos_37_pd                        -2.257402e-05  2.565877e-06  2.770578e-05
## pos_38_pd                        -3.728036e-05  1.193187e-06  3.966674e-05
## pos_39_pd                        -5.796019e-05 -2.043583e-06  5.387302e-05
##                                       sd_coef
## (Intercept)                      3.814563e-06
## StateAlaska                      4.425723e-06
## StateArizona                     3.424942e-06
## StateArkansas                    3.518699e-06
## StateCalifornia                  4.664966e-06
## StateColorado                    3.765454e-06
## StateConnecticut                 4.334932e-06
## StateDelaware                    6.377363e-06
## StateFlorida                     3.159778e-06
## StateGeorgia                     3.414173e-06
## StateHawaii                      4.427232e-06
## StateIdaho                       3.273268e-06
## StateIllinois                    3.586053e-06
## StateIndiana                     2.886312e-06
## StateIowa                        2.909185e-06
## StateKansas                      2.810304e-06
## StateKentucky                    3.984269e-06
## StateLouisiana                   3.189040e-06
## StateMaine                       5.346331e-06
## StateMaryland                    3.683666e-06
## StateMassachusetts               5.191326e-06
## StateMichigan                    2.875832e-06
## StateMinnesota                   3.928350e-06
## StateMississippi                 3.391612e-06
## StateMissouri                    3.017809e-06
## StateMontana                     4.552719e-06
## StateNebraska                    3.106793e-06
## StateNevada                      4.120796e-06
## StateNew Hampshire               5.223727e-06
## StateNew Jersey                  4.419316e-06
## StateNew Mexico                  5.115691e-06
## StateNew York                    3.279234e-06
## StateNorth Carolina              2.735505e-06
## StateNorth Dakota                4.142472e-06
## StateOhio                        6.526905e-06
## StateOklahoma                    4.030604e-06
## StateOregon                      3.898352e-06
## StatePennsylvania                4.167985e-06
## StateRhode Island                4.826761e-06
## StateSouth Carolina              2.733795e-06
## StateSouth Dakota                3.440939e-06
## StateTennessee                   3.600999e-06
## StateTexas                       3.893272e-06
## StateUtah                        3.425881e-06
## StateVermont                     3.948464e-06
## StateVirginia                    2.600359e-06
## StateWashington                  4.085411e-06
## StateWest Virginia               8.968262e-06
## StateWisconsin                   2.765576e-06
## StateWyoming                     3.525699e-06
## factor(Time_Period_ID)2          4.479111e-06
## factor(Time_Period_ID)3          4.359504e-06
## factor(Time_Period_ID)4          4.366498e-06
## factor(Time_Period_ID)5          4.373944e-06
## factor(Time_Period_ID)6          4.240968e-06
## factor(Time_Period_ID)7          4.165165e-06
## factor(Time_Period_ID)8          4.153250e-06
## factor(Time_Period_ID)9          4.030838e-06
## factor(Time_Period_ID)10         4.056516e-06
## factor(Time_Period_ID)11         3.927176e-06
## factor(Time_Period_ID)12         4.375606e-06
## factor(Time_Period_ID)13         3.973825e-06
## factor(Time_Period_ID)14         4.000199e-06
## factor(Time_Period_ID)15         4.096365e-06
## factor(Time_Period_ID)16         4.022204e-06
## factor(Time_Period_ID)17         4.221713e-06
## factor(Time_Period_ID)18         4.045886e-06
## factor(Time_Period_ID)19         4.930037e-06
## factor(Time_Period_ID)20         4.471565e-06
## factor(Time_Period_ID)21         4.290636e-06
## factor(Time_Period_ID)22         4.433577e-06
## factor(Time_Period_ID)23         4.447340e-06
## factor(Time_Period_ID)24         4.615439e-06
## factor(Time_Period_ID)25         4.658132e-06
## factor(Time_Period_ID)26         4.649822e-06
## factor(Time_Period_ID)27         4.674470e-06
## factor(Time_Period_ID)28         4.757770e-06
## factor(Time_Period_ID)29         4.929440e-06
## factor(Time_Period_ID)30         5.175423e-06
## factor(Time_Period_ID)31         5.261004e-06
## factor(Time_Period_ID)32         5.541948e-06
## factor(Time_Period_ID)33         6.088352e-06
## factor(Time_Period_ID)34         6.632834e-06
## factor(Time_Period_ID)35         7.770996e-06
## factor(Time_Period_ID)36         7.342010e-06
## factor(Time_Period_ID)37         7.154032e-06
## factor(Time_Period_ID)38         7.630668e-06
## factor(Time_Period_ID)39         7.212216e-06
## factor(Time_Period_ID)40         8.042636e-06
## Naloxone_Pharmacy_Yes_Redefined  3.046313e-06
## Naloxone_Pharmacy_No_Redefined   2.418179e-06
## Medical_Marijuana_Redefined      2.533552e-06
## Recreational_Marijuana_Redefined 4.360117e-06
## GSL_Redefined                    2.285130e-06
## PDMP_Redefined                   1.708801e-06
## Medicaid_Expansion_Redefined     2.315953e-06
## pos_0_pd                         2.446511e-06
## pos_1_pd                         2.955928e-06
## pos_2_pd                         2.954534e-06
## pos_3_pd                         3.158775e-06
## pos_4_pd                         3.512971e-06
## pos_5_pd                         3.372958e-06
## pos_6_pd                         3.878289e-06
## pos_7_pd                         3.654312e-06
## pos_8_pd                         4.128761e-06
## pos_9_pd                         3.639312e-06
## pos_10_pd                        3.807446e-06
## pos_11_pd                        3.683914e-06
## pos_12_pd                        3.522826e-06
## pos_13_pd                        4.200970e-06
## pos_14_pd                        3.845182e-06
## pos_15_pd                        4.449530e-06
## pos_16_pd                        4.468810e-06
## pos_17_pd                        5.405708e-06
## pos_18_pd                        4.910673e-06
## pos_19_pd                        4.386994e-06
## pos_20_pd                        4.706816e-06
## pos_21_pd                        4.807146e-06
## pos_22_pd                        5.031086e-06
## pos_23_pd                        5.701225e-06
## pos_24_pd                        5.083725e-06
## pos_25_pd                        5.607166e-06
## pos_26_pd                        5.747227e-06
## pos_27_pd                        5.865254e-06
## pos_28_pd                        6.368261e-06
## pos_29_pd                        7.718237e-06
## pos_30_pd                        7.848702e-06
## pos_31_pd                        1.051970e-05
## pos_32_pd                        1.379801e-05
## pos_33_pd                        1.365257e-05
## pos_34_pd                        1.687793e-05
## pos_35_pd                        1.238155e-05
## pos_36_pd                        9.520503e-06
## pos_37_pd                        1.282648e-05
## pos_38_pd                        1.962936e-05
## pos_39_pd                        2.852888e-05

6.3.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_fixed_time <- sensitivity_anlys_post_tx_sd_and_ci_fixed_time %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_fixed_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_fixed_time$num_states <- sapply(plot_post_tx_fixed_time$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx_fixed_time, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_vline(aes(xintercept = coef(main_analysis_model_fixed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
  geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_fixed_time)["Intervention_Redefined"]), y = 12, 
            x = coef(main_analysis_model_fixed_time)["Intervention_Redefined"] + 0.00001), color = "red")

  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

7 OLS Model Main Analysis With Smoothed Time Effects With Log Proportion

#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population

#fit an OLS with smoothed time effects
main_analysis_model_log_smoothed_time<-gam(log(prop_dead)~ State +
                           s(Time_Period_ID, bs = "cr", by = as.factor(Region)) +
                           Naloxone_Pharmacy_Yes_Redefined +
                           Naloxone_Pharmacy_No_Redefined +
                           Medical_Marijuana_Redefined +
                           Recreational_Marijuana_Redefined +
                           GSL_Redefined +
                           PDMP_Redefined +
                           Medicaid_Expansion_Redefined +
                           Intervention_Redefined ,
                         data = main_analysis_data)

summary(main_analysis_model_log_smoothed_time)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     Intervention_Redefined
## 
## Parametric coefficients:
##                                   Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -9.711293   0.052777 -184.006  < 2e-16 ***
## StateAlaska                       0.164106   0.074380    2.206 0.027480 *  
## StateArizona                      0.288302   0.067744    4.256 2.18e-05 ***
## StateArkansas                    -0.487283   0.066740   -7.301 4.16e-13 ***
## StateCalifornia                  -0.155692   0.074371   -2.093 0.036440 *  
## StateColorado                     0.035981   0.074125    0.485 0.627444    
## StateConnecticut                  0.230076   0.070893    3.245 0.001193 ** 
## StateDelaware                     0.216431   0.067992    3.183 0.001480 ** 
## StateFlorida                      0.309018   0.066797    4.626 3.97e-06 ***
## StateGeorgia                      0.000433   0.066781    0.006 0.994827    
## StateHawaii                      -0.378239   0.072961   -5.184 2.40e-07 ***
## StateIdaho                       -0.124420   0.066788   -1.863 0.062628 .  
## StateIllinois                     0.161001   0.067802    2.375 0.017667 *  
## StateIndiana                      0.081619   0.066357    1.230 0.218845    
## StateIowa                        -0.676997   0.066568  -10.170  < 2e-16 ***
## StateKansas                      -0.230527   0.066060   -3.490 0.000495 ***
## StateKentucky                     0.702316   0.066783   10.516  < 2e-16 ***
## StateLouisiana                    0.340740   0.065973    5.165 2.66e-07 ***
## StateMaine                        0.088824   0.073874    1.202 0.229369    
## StateMaryland                    -1.513084   0.067786  -22.321  < 2e-16 ***
## StateMassachusetts               -0.083599   0.067340   -1.241 0.214593    
## StateMichigan                     0.010429   0.068383    0.153 0.878801    
## StateMinnesota                   -0.643068   0.069892   -9.201  < 2e-16 ***
## StateMississippi                 -0.049288   0.066014   -0.747 0.455380    
## StateMissouri                     0.167659   0.068266    2.456 0.014138 *  
## StateMontana                     -0.439514   0.070271   -6.255 4.90e-10 ***
## StateNebraska                    -0.874032   0.067084  -13.029  < 2e-16 ***
## StateNevada                       0.460178   0.071746    6.414 1.78e-10 ***
## StateNew Hampshire                0.147406   0.067147    2.195 0.028264 *  
## StateNew Jersey                   0.080613   0.067947    1.186 0.235611    
## StateNew Mexico                   0.645396   0.072906    8.852  < 2e-16 ***
## StateNew York                    -0.139492   0.068359   -2.041 0.041429 *  
## StateNorth Carolina               0.233840   0.065853    3.551 0.000393 ***
## StateNorth Dakota                -1.137555   0.066451  -17.119  < 2e-16 ***
## StateOhio                         0.452817   0.066969    6.762 1.80e-11 ***
## StateOklahoma                     0.464010   0.066457    6.982 3.99e-12 ***
## StateOregon                      -0.271552   0.073846   -3.677 0.000242 ***
## StatePennsylvania                 0.561023   0.066850    8.392  < 2e-16 ***
## StateRhode Island                -0.278774   0.069373   -4.018 6.08e-05 ***
## StateSouth Carolina               0.207544   0.066391    3.126 0.001798 ** 
## StateSouth Dakota                -1.027424   0.066779  -15.386  < 2e-16 ***
## StateTennessee                    0.468655   0.065670    7.136 1.35e-12 ***
## StateTexas                       -0.019383   0.066729   -0.290 0.771481    
## StateUtah                        -0.095477   0.066061   -1.445 0.148542    
## StateVermont                     -0.169566   0.069677   -2.434 0.015041 *  
## StateVirginia                    -0.032103   0.065975   -0.487 0.626602    
## StateWashington                   0.045026   0.075228    0.599 0.549557    
## StateWest Virginia                0.790500   0.066804   11.833  < 2e-16 ***
## StateWisconsin                    0.006409   0.066116    0.097 0.922789    
## StateWyoming                     -0.021573   0.066041   -0.327 0.743956    
## Naloxone_Pharmacy_Yes_Redefined  -0.078516   0.042517   -1.847 0.064946 .  
## Naloxone_Pharmacy_No_Redefined   -0.001783   0.038500   -0.046 0.963069    
## Medical_Marijuana_Redefined       0.192033   0.030656    6.264 4.62e-10 ***
## Recreational_Marijuana_Redefined -0.110335   0.048796   -2.261 0.023863 *  
## GSL_Redefined                     0.054084   0.031598    1.712 0.087127 .  
## PDMP_Redefined                   -0.152943   0.024680   -6.197 7.02e-10 ***
## Medicaid_Expansion_Redefined      0.091989   0.030149    3.051 0.002311 ** 
## Intervention_Redefined           -0.026254   0.024341   -1.079 0.280903    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df      F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   4.779  5.836 140.15  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.464  8.917  82.99  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     6.300  7.442 105.57  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      3.355  4.185  86.33  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.84   Deviance explained = 84.6%
## GCV = 0.089598  Scale est. = 0.085974  n = 2000
gam.check(main_analysis_model_log_smoothed_time, page = 1)

## 
## Method: GCV   Optimizer: magic
## Smoothing parameter selection converged after 5 iterations.
## The RMS GCV score gradient at convergence was 1.134567e-06 .
## The Hessian was positive definite.
## Model rank =  94 / 94 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                                                k'  edf k-index p-value
## s(Time_Period_ID):as.factor(Region)Midwest   9.00 4.78    1.05    0.98
## s(Time_Period_ID):as.factor(Region)Northeast 9.00 8.46    1.05    0.98
## s(Time_Period_ID):as.factor(Region)South     9.00 6.30    1.05    0.99
## s(Time_Period_ID):as.factor(Region)West      9.00 3.36    1.05    1.00
#examine fitted values
summary(fitted(main_analysis_model_log_smoothed_time))
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -12.314 -10.207  -9.739  -9.796  -9.341  -8.122
hist(fitted(main_analysis_model_log_smoothed_time))

#smoothed effects
plot(main_analysis_model_log_smoothed_time, pages = 1)

7.1 Coefficients and 95% CI

#compute the full dataset including basis functions
full_df_w_basis_functions_log_smoothed_time <- as.matrix(data.frame(predict(main_analysis_model_log_smoothed_time, type = "lpmatrix")))

#estimate the 95% CI and SD
coefficient_values_log_smoothed_time <- coef(main_analysis_model_log_smoothed_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_smoothed_time <- compute_sd_and_CI(full_df_w_basis_functions_log_smoothed_time,
                                                               log(main_analysis_data$prop_dead),
                                                               coefficient_values_log_smoothed_time,
                                                               p = ncol(full_df_w_basis_functions_log_smoothed_time) - 50)
round(main_analysis_sd_and_ci_log_smoothed_time, 3)
##                                                lb_coef coef_values ub_coef
## (Intercept)                                     -9.800      -9.711  -9.622
## StateAlaska                                      0.040       0.164   0.289
## StateArizona                                     0.193       0.288   0.384
## StateArkansas                                   -0.600      -0.487  -0.375
## StateCalifornia                                 -0.274      -0.156  -0.037
## StateColorado                                   -0.074       0.036   0.146
## StateConnecticut                                 0.097       0.230   0.363
## StateDelaware                                    0.094       0.216   0.339
## StateFlorida                                     0.205       0.309   0.413
## StateGeorgia                                    -0.085       0.000   0.086
## StateHawaii                                     -0.496      -0.378  -0.260
## StateIdaho                                      -0.220      -0.124  -0.029
## StateIllinois                                    0.039       0.161   0.283
## StateIndiana                                    -0.020       0.082   0.183
## StateIowa                                       -0.770      -0.677  -0.584
## StateKansas                                     -0.327      -0.231  -0.134
## StateKentucky                                    0.616       0.702   0.788
## StateLouisiana                                   0.248       0.341   0.433
## StateMaine                                      -0.043       0.089   0.221
## StateMaryland                                   -1.719      -1.513  -1.308
## StateMassachusetts                              -0.297      -0.084   0.129
## StateMichigan                                   -0.083       0.010   0.104
## StateMinnesota                                  -0.746      -0.643  -0.540
## StateMississippi                                -0.143      -0.049   0.044
## StateMissouri                                    0.077       0.168   0.259
## StateMontana                                    -0.547      -0.440  -0.332
## StateNebraska                                   -0.969      -0.874  -0.779
## StateNevada                                      0.349       0.460   0.571
## StateNew Hampshire                               0.040       0.147   0.255
## StateNew Jersey                                 -0.075       0.081   0.236
## StateNew Mexico                                  0.517       0.645   0.774
## StateNew York                                   -0.257      -0.139  -0.022
## StateNorth Carolina                              0.154       0.234   0.314
## StateNorth Dakota                               -1.293      -1.138  -0.982
## StateOhio                                        0.354       0.453   0.552
## StateOklahoma                                    0.354       0.464   0.574
## StateOregon                                     -0.382      -0.272  -0.161
## StatePennsylvania                                0.456       0.561   0.666
## StateRhode Island                               -0.581      -0.279   0.023
## StateSouth Carolina                              0.119       0.208   0.296
## StateSouth Dakota                               -1.149      -1.027  -0.906
## StateTennessee                                   0.388       0.469   0.549
## StateTexas                                      -0.131      -0.019   0.093
## StateUtah                                       -0.258      -0.095   0.067
## StateVermont                                    -0.306      -0.170  -0.033
## StateVirginia                                   -0.127      -0.032   0.062
## StateWashington                                 -0.071       0.045   0.161
## StateWest Virginia                               0.650       0.791   0.931
## StateWisconsin                                  -0.075       0.006   0.088
## StateWyoming                                    -0.148      -0.022   0.105
## Naloxone_Pharmacy_Yes_Redefined                 -0.144      -0.079  -0.013
## Naloxone_Pharmacy_No_Redefined                  -0.066      -0.002   0.062
## Medical_Marijuana_Redefined                      0.125       0.192   0.259
## Recreational_Marijuana_Redefined                -0.182      -0.110  -0.039
## GSL_Redefined                                    0.000       0.054   0.108
## PDMP_Redefined                                  -0.206      -0.153  -0.100
## Medicaid_Expansion_Redefined                     0.041       0.092   0.143
## Intervention_Redefined                          -0.072      -0.026   0.020
## s(Time_Period_ID):as.factor(Region)Midwest.1    -0.542      -0.441  -0.340
## s(Time_Period_ID):as.factor(Region)Midwest.2    -0.249      -0.170  -0.091
## s(Time_Period_ID):as.factor(Region)Midwest.3     0.051       0.135   0.220
## s(Time_Period_ID):as.factor(Region)Midwest.4     0.259       0.343   0.427
## s(Time_Period_ID):as.factor(Region)Midwest.5     0.393       0.473   0.554
## s(Time_Period_ID):as.factor(Region)Midwest.6     0.546       0.625   0.704
## s(Time_Period_ID):as.factor(Region)Midwest.7     0.727       0.806   0.885
## s(Time_Period_ID):as.factor(Region)Midwest.8     0.941       1.032   1.123
## s(Time_Period_ID):as.factor(Region)Midwest.9     0.848       0.944   1.039
## s(Time_Period_ID):as.factor(Region)Northeast.1  -0.777      -0.474  -0.171
## s(Time_Period_ID):as.factor(Region)Northeast.2  -0.527      -0.297  -0.066
## s(Time_Period_ID):as.factor(Region)Northeast.3   0.183       0.362   0.540
## s(Time_Period_ID):as.factor(Region)Northeast.4   0.106       0.279   0.452
## s(Time_Period_ID):as.factor(Region)Northeast.5   0.186       0.359   0.532
## s(Time_Period_ID):as.factor(Region)Northeast.6   0.395       0.553   0.711
## s(Time_Period_ID):as.factor(Region)Northeast.7   0.731       0.895   1.059
## s(Time_Period_ID):as.factor(Region)Northeast.8   1.142       1.314   1.486
## s(Time_Period_ID):as.factor(Region)Northeast.9   0.897       1.050   1.203
## s(Time_Period_ID):as.factor(Region)South.1      -0.426      -0.341  -0.256
## s(Time_Period_ID):as.factor(Region)South.2      -0.159      -0.089  -0.020
## s(Time_Period_ID):as.factor(Region)South.3       0.084       0.166   0.248
## s(Time_Period_ID):as.factor(Region)South.4       0.242       0.319   0.395
## s(Time_Period_ID):as.factor(Region)South.5       0.375       0.441   0.507
## s(Time_Period_ID):as.factor(Region)South.6       0.480       0.549   0.618
## s(Time_Period_ID):as.factor(Region)South.7       0.659       0.736   0.813
## s(Time_Period_ID):as.factor(Region)South.8       0.885       0.992   1.100
## s(Time_Period_ID):as.factor(Region)South.9       0.690       0.827   0.965
## s(Time_Period_ID):as.factor(Region)West.1       -0.373      -0.270  -0.167
## s(Time_Period_ID):as.factor(Region)West.2       -0.163      -0.083  -0.004
## s(Time_Period_ID):as.factor(Region)West.3        0.034       0.115   0.196
## s(Time_Period_ID):as.factor(Region)West.4        0.194       0.263   0.332
## s(Time_Period_ID):as.factor(Region)West.5        0.290       0.362   0.434
## s(Time_Period_ID):as.factor(Region)West.6        0.356       0.438   0.519
## s(Time_Period_ID):as.factor(Region)West.7        0.414       0.503   0.592
## s(Time_Period_ID):as.factor(Region)West.8        0.514       0.626   0.738
## s(Time_Period_ID):as.factor(Region)West.9        0.490       0.588   0.685
##                                                sd_coef
## (Intercept)                                      0.045
## StateAlaska                                      0.063
## StateArizona                                     0.049
## StateArkansas                                    0.058
## StateCalifornia                                  0.060
## StateColorado                                    0.056
## StateConnecticut                                 0.068
## StateDelaware                                    0.063
## StateFlorida                                     0.053
## StateGeorgia                                     0.044
## StateHawaii                                      0.060
## StateIdaho                                       0.049
## StateIllinois                                    0.062
## StateIndiana                                     0.052
## StateIowa                                        0.047
## StateKansas                                      0.049
## StateKentucky                                    0.044
## StateLouisiana                                   0.047
## StateMaine                                       0.067
## StateMaryland                                    0.105
## StateMassachusetts                               0.109
## StateMichigan                                    0.048
## StateMinnesota                                   0.052
## StateMississippi                                 0.048
## StateMissouri                                    0.046
## StateMontana                                     0.055
## StateNebraska                                    0.048
## StateNevada                                      0.057
## StateNew Hampshire                               0.055
## StateNew Jersey                                  0.079
## StateNew Mexico                                  0.065
## StateNew York                                    0.060
## StateNorth Carolina                              0.041
## StateNorth Dakota                                0.079
## StateOhio                                        0.050
## StateOklahoma                                    0.056
## StateOregon                                      0.056
## StatePennsylvania                                0.054
## StateRhode Island                                0.154
## StateSouth Carolina                              0.045
## StateSouth Dakota                                0.062
## StateTennessee                                   0.041
## StateTexas                                       0.057
## StateUtah                                        0.083
## StateVermont                                     0.070
## StateVirginia                                    0.048
## StateWashington                                  0.059
## StateWest Virginia                               0.072
## StateWisconsin                                   0.042
## StateWyoming                                     0.064
## Naloxone_Pharmacy_Yes_Redefined                  0.034
## Naloxone_Pharmacy_No_Redefined                   0.033
## Medical_Marijuana_Redefined                      0.034
## Recreational_Marijuana_Redefined                 0.036
## GSL_Redefined                                    0.028
## PDMP_Redefined                                   0.027
## Medicaid_Expansion_Redefined                     0.026
## Intervention_Redefined                           0.023
## s(Time_Period_ID):as.factor(Region)Midwest.1     0.052
## s(Time_Period_ID):as.factor(Region)Midwest.2     0.040
## s(Time_Period_ID):as.factor(Region)Midwest.3     0.043
## s(Time_Period_ID):as.factor(Region)Midwest.4     0.043
## s(Time_Period_ID):as.factor(Region)Midwest.5     0.041
## s(Time_Period_ID):as.factor(Region)Midwest.6     0.040
## s(Time_Period_ID):as.factor(Region)Midwest.7     0.040
## s(Time_Period_ID):as.factor(Region)Midwest.8     0.047
## s(Time_Period_ID):as.factor(Region)Midwest.9     0.049
## s(Time_Period_ID):as.factor(Region)Northeast.1   0.155
## s(Time_Period_ID):as.factor(Region)Northeast.2   0.117
## s(Time_Period_ID):as.factor(Region)Northeast.3   0.091
## s(Time_Period_ID):as.factor(Region)Northeast.4   0.088
## s(Time_Period_ID):as.factor(Region)Northeast.5   0.088
## s(Time_Period_ID):as.factor(Region)Northeast.6   0.081
## s(Time_Period_ID):as.factor(Region)Northeast.7   0.084
## s(Time_Period_ID):as.factor(Region)Northeast.8   0.088
## s(Time_Period_ID):as.factor(Region)Northeast.9   0.078
## s(Time_Period_ID):as.factor(Region)South.1       0.043
## s(Time_Period_ID):as.factor(Region)South.2       0.036
## s(Time_Period_ID):as.factor(Region)South.3       0.042
## s(Time_Period_ID):as.factor(Region)South.4       0.039
## s(Time_Period_ID):as.factor(Region)South.5       0.034
## s(Time_Period_ID):as.factor(Region)South.6       0.035
## s(Time_Period_ID):as.factor(Region)South.7       0.039
## s(Time_Period_ID):as.factor(Region)South.8       0.055
## s(Time_Period_ID):as.factor(Region)South.9       0.070
## s(Time_Period_ID):as.factor(Region)West.1        0.053
## s(Time_Period_ID):as.factor(Region)West.2        0.041
## s(Time_Period_ID):as.factor(Region)West.3        0.041
## s(Time_Period_ID):as.factor(Region)West.4        0.035
## s(Time_Period_ID):as.factor(Region)West.5        0.037
## s(Time_Period_ID):as.factor(Region)West.6        0.041
## s(Time_Period_ID):as.factor(Region)West.7        0.046
## s(Time_Period_ID):as.factor(Region)West.8        0.057
## s(Time_Period_ID):as.factor(Region)West.9        0.050

7.1.1 Attributable Deaths

date_data <- main_analysis_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_smoothed_time <- attr_death_compute(main_analysis_data, main_analysis_sd_and_ci_log_smoothed_time, 
                                                        post_tx_model = FALSE, tx_name = "Intervention_Redefined")
attr_deaths_est_log_smoothed_time <- merge(attr_deaths_est_log_smoothed_time, date_data, by.x = "Time_Period", by.y = "Time_Period_ID")

ggplot(attr_deaths_est_log_smoothed_time, aes(x = Time_Period_Start)) + 
  # geom_point(aes(y = attr_deaths)) + 
  geom_line(aes(y = attr_deaths, linetype = "Estimate")) + 
  # geom_point(aes(y = attr_deaths_lb)) + 
  geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) + 
  # geom_point(aes(y = attr_deaths_ub)) + 
  geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) + 
  labs(x = "Date", y = "Attributable Deaths",
       title = "Estimated Number of Attributable Deaths Using Smoothed Time Effects, 
       Log Probability of Drug Overdose Death",
       linetype = "") + 
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black")) + 
  scale_linetype_manual(values = c("dashed", "solid"))

7.2 Event Study

7.2.1 Model Fitting

#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures, 
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention

formula_event_study_log_smoothed_time <- formula(paste("log(prop_dead) ~ State +
                                           s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2), 
                                            function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
                                     "+",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_log_smoothed_time<-gam(formula_event_study_log_smoothed_time,
                                         data = sensitivity_anlys_event_study_data)

summary(sensitivity_anlys_event_study_model_log_smoothed_time)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     neg_2_pd + neg_3_pd + neg_4_pd + neg_5_pd + neg_6_pd + neg_7_pd + 
##     neg_8_pd + neg_9_pd + neg_10_pd + neg_11_pd + neg_12_pd + 
##     neg_13_pd + neg_14_pd + neg_15_pd + neg_16_pd + neg_17_pd + 
##     neg_18_pd + neg_19_pd + neg_20_pd + neg_21_pd + neg_22_pd + 
##     neg_23_pd + neg_24_pd + neg_25_pd + neg_26_pd + neg_27_pd + 
##     neg_28_pd + neg_29_pd + neg_30_pd + neg_31_pd + neg_32_pd + 
##     neg_33_pd + pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + 
##     pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + 
##     pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + 
##     pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + 
##     pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + 
##     pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd + 
##     pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd + 
##     pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd
## 
## Parametric coefficients:
##                                   Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -9.607755   0.067863 -141.576  < 2e-16 ***
## StateAlaska                       0.101715   0.098217    1.036 0.300517    
## StateArizona                      0.257887   0.075570    3.413 0.000657 ***
## StateArkansas                    -0.516039   0.070907   -7.278 5.00e-13 ***
## StateCalifornia                  -0.062450   0.087003   -0.718 0.472974    
## StateColorado                     0.002447   0.080071    0.031 0.975619    
## StateConnecticut                  0.222377   0.070209    3.167 0.001563 ** 
## StateDelaware                     0.155066   0.093602    1.657 0.097760 .  
## StateFlorida                      0.412925   0.085633    4.822 1.54e-06 ***
## StateGeorgia                      0.127610   0.091409    1.396 0.162873    
## StateHawaii                      -0.467150   0.085022   -5.494 4.46e-08 ***
## StateIdaho                       -0.159067   0.088201   -1.803 0.071480 .  
## StateIllinois                     0.233582   0.078669    2.969 0.003024 ** 
## StateIndiana                      0.076072   0.067464    1.128 0.259638    
## StateIowa                        -0.624313   0.071621   -8.717  < 2e-16 ***
## StateKansas                      -0.224553   0.065504   -3.428 0.000621 ***
## StateKentucky                     0.686996   0.071398    9.622  < 2e-16 ***
## StateLouisiana                    0.394888   0.072472    5.449 5.75e-08 ***
## StateMaine                        0.074858   0.074340    1.007 0.314085    
## StateMaryland                    -1.451852   0.079818  -18.190  < 2e-16 ***
## StateMassachusetts               -0.083063   0.066635   -1.247 0.212728    
## StateMichigan                     0.050577   0.069988    0.723 0.469989    
## StateMinnesota                   -0.645251   0.069319   -9.308  < 2e-16 ***
## StateMississippi                 -0.087269   0.082265   -1.061 0.288911    
## StateMissouri                     0.185703   0.070874    2.620 0.008860 ** 
## StateMontana                     -0.394332   0.075905   -5.195 2.27e-07 ***
## StateNebraska                    -0.912235   0.076218  -11.969  < 2e-16 ***
## StateNevada                       0.495673   0.072891    6.800 1.41e-11 ***
## StateNew Hampshire                0.124592   0.068078    1.830 0.067391 .  
## StateNew Jersey                   0.145728   0.079490    1.833 0.066922 .  
## StateNew Mexico                   0.622211   0.074154    8.391  < 2e-16 ***
## StateNew York                    -0.132280   0.067726   -1.953 0.050950 .  
## StateNorth Carolina               0.274412   0.069114    3.970 7.45e-05 ***
## StateNorth Dakota                -1.172708   0.075925  -15.446  < 2e-16 ***
## StateOhio                         0.589152   0.091264    6.455 1.37e-10 ***
## StateOklahoma                     0.453117   0.070142    6.460 1.33e-10 ***
## StateOregon                      -0.299060   0.074811   -3.998 6.65e-05 ***
## StatePennsylvania                 0.677460   0.085176    7.954 3.13e-15 ***
## StateRhode Island                -0.312528   0.083915   -3.724 0.000202 ***
## StateSouth Carolina               0.161134   0.089821    1.794 0.072984 .  
## StateSouth Dakota                -1.084871   0.092931  -11.674  < 2e-16 ***
## StateTennessee                    0.470730   0.064928    7.250 6.10e-13 ***
## StateTexas                        0.087488   0.082520    1.060 0.289191    
## StateUtah                        -0.054042   0.067959   -0.795 0.426594    
## StateVermont                     -0.191088   0.070367   -2.716 0.006677 ** 
## StateVirginia                     0.031406   0.073798    0.426 0.670476    
## StateWashington                   0.024086   0.075003    0.321 0.748139    
## StateWest Virginia                0.763862   0.076548    9.979  < 2e-16 ***
## StateWisconsin                    0.055351   0.072662    0.762 0.446302    
## StateWyoming                     -0.026862   0.066431   -0.404 0.685993    
## Naloxone_Pharmacy_Yes_Redefined  -0.061320   0.042077   -1.457 0.145198    
## Naloxone_Pharmacy_No_Redefined    0.003373   0.038423    0.088 0.930048    
## Medical_Marijuana_Redefined       0.199071   0.030945    6.433 1.59e-10 ***
## Recreational_Marijuana_Redefined -0.098627   0.049132   -2.007 0.044856 *  
## GSL_Redefined                     0.063283   0.031502    2.009 0.044694 *  
## PDMP_Redefined                   -0.178714   0.024902   -7.177 1.03e-12 ***
## Medicaid_Expansion_Redefined      0.089196   0.030306    2.943 0.003289 ** 
## neg_2_pd                          0.020525   0.059558    0.345 0.730419    
## neg_3_pd                          0.016757   0.060521    0.277 0.781904    
## neg_4_pd                         -0.010784   0.061849   -0.174 0.861604    
## neg_5_pd                         -0.013005   0.062636   -0.208 0.835542    
## neg_6_pd                         -0.005779   0.064769   -0.089 0.928918    
## neg_7_pd                         -0.044022   0.065888   -0.668 0.504133    
## neg_8_pd                         -0.100544   0.067553   -1.488 0.136824    
## neg_9_pd                         -0.025159   0.070355   -0.358 0.720682    
## neg_10_pd                         0.024031   0.072377    0.332 0.739905    
## neg_11_pd                         0.025412   0.074678    0.340 0.733676    
## neg_12_pd                         0.115436   0.078970    1.462 0.143974    
## neg_13_pd                         0.015177   0.080972    0.187 0.851337    
## neg_14_pd                        -0.015730   0.083077   -0.189 0.849848    
## neg_15_pd                        -0.059495   0.085395   -0.697 0.486076    
## neg_16_pd                        -0.043767   0.089648   -0.488 0.625457    
## neg_17_pd                        -0.060151   0.094770   -0.635 0.525694    
## neg_18_pd                        -0.051908   0.098163   -0.529 0.597012    
## neg_19_pd                        -0.154364   0.101364   -1.523 0.127962    
## neg_20_pd                        -0.193711   0.107211   -1.807 0.070952 .  
## neg_21_pd                        -0.117693   0.114201   -1.031 0.302874    
## neg_22_pd                        -0.096424   0.116856   -0.825 0.409392    
## neg_23_pd                        -0.116591   0.121027   -0.963 0.335499    
## neg_24_pd                        -0.180864   0.130018   -1.391 0.164370    
## neg_25_pd                        -0.038789   0.132443   -0.293 0.769652    
## neg_26_pd                         0.044238   0.138129    0.320 0.748801    
## neg_27_pd                        -0.213628   0.153601   -1.391 0.164454    
## neg_28_pd                        -0.201311   0.156228   -1.289 0.197708    
## neg_29_pd                         0.024088   0.164854    0.146 0.883844    
## neg_30_pd                        -0.052096   0.175256   -0.297 0.766303    
## neg_31_pd                        -0.054179   0.177815   -0.305 0.760633    
## neg_32_pd                         0.032863   0.192904    0.170 0.864746    
## neg_33_pd                         0.109008   0.244825    0.445 0.656193    
## pos_0_pd                         -0.011150   0.059300   -0.188 0.850881    
## pos_1_pd                         -0.040114   0.059907   -0.670 0.503195    
## pos_2_pd                         -0.005207   0.060753   -0.086 0.931707    
## pos_3_pd                         -0.041494   0.061831   -0.671 0.502250    
## pos_4_pd                         -0.047126   0.063088   -0.747 0.455163    
## pos_5_pd                         -0.092046   0.064554   -1.426 0.154073    
## pos_6_pd                         -0.097121   0.066353   -1.464 0.143447    
## pos_7_pd                         -0.094524   0.068293   -1.384 0.166498    
## pos_8_pd                         -0.140579   0.070834   -1.985 0.047333 *  
## pos_9_pd                         -0.162175   0.073212   -2.215 0.026873 *  
## pos_10_pd                        -0.180017   0.075305   -2.390 0.016926 *  
## pos_11_pd                        -0.183783   0.077902   -2.359 0.018419 *  
## pos_12_pd                        -0.193796   0.080631   -2.403 0.016337 *  
## pos_13_pd                        -0.262320   0.083119   -3.156 0.001626 ** 
## pos_14_pd                        -0.247336   0.086650   -2.854 0.004359 ** 
## pos_15_pd                        -0.250438   0.089880   -2.786 0.005385 ** 
## pos_16_pd                        -0.268524   0.092766   -2.895 0.003840 ** 
## pos_17_pd                        -0.263062   0.096568   -2.724 0.006508 ** 
## pos_18_pd                        -0.253664   0.099917   -2.539 0.011207 *  
## pos_19_pd                        -0.243608   0.102661   -2.373 0.017749 *  
## pos_20_pd                        -0.247583   0.106915   -2.316 0.020683 *  
## pos_21_pd                        -0.274332   0.111178   -2.468 0.013696 *  
## pos_22_pd                        -0.266750   0.114684   -2.326 0.020129 *  
## pos_23_pd                        -0.273338   0.118731   -2.302 0.021437 *  
## pos_24_pd                        -0.310855   0.123993   -2.507 0.012260 *  
## pos_25_pd                        -0.279921   0.129223   -2.166 0.030424 *  
## pos_26_pd                        -0.289984   0.132325   -2.191 0.028544 *  
## pos_27_pd                        -0.338309   0.135880   -2.490 0.012870 *  
## pos_28_pd                        -0.321207   0.138889   -2.313 0.020849 *  
## pos_29_pd                        -0.334409   0.146219   -2.287 0.022306 *  
## pos_30_pd                        -0.285008   0.150706   -1.891 0.058760 .  
## pos_31_pd                        -0.241546   0.155923   -1.549 0.121520    
## pos_32_pd                        -0.298667   0.165839   -1.801 0.071875 .  
## pos_33_pd                        -0.326206   0.172025   -1.896 0.058080 .  
## pos_34_pd                        -0.314276   0.175300   -1.793 0.073169 .  
## pos_35_pd                        -0.514644   0.191451   -2.688 0.007250 ** 
## pos_36_pd                        -0.541251   0.194692   -2.780 0.005490 ** 
## pos_37_pd                        -0.534988   0.216760   -2.468 0.013673 *  
## pos_38_pd                        -0.513830   0.263987   -1.946 0.051755 .  
## pos_39_pd                        -0.534088   0.267298   -1.998 0.045852 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df     F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   4.324  5.320 41.55  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.377  8.891 30.51  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     5.950  7.101 27.09  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      3.005  3.768 28.00  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.844   Deviance explained = 85.5%
## GCV = 0.09088  Scale est. = 0.084034  n = 2000

7.2.2 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_log_smoothed_time <-
  data.frame(predict(sensitivity_anlys_event_study_model_log_smoothed_time, type = "lpmatrix"))

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_log_smoothed_time <- coef(sensitivity_anlys_event_study_model_log_smoothed_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time <-
  compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_event_study_log_smoothed_time), 
                                                             log(sensitivity_anlys_event_study_data$prop_dead),
                                                             coefficient_values_sensitivity_anlys_event_study_log_smoothed_time,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_log_smoothed_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time)
##                                                     lb_coef  coef_values
## (Intercept)                                    -9.728823888 -9.607755377
## StateAlaska                                    -0.047405904  0.101715259
## StateArizona                                    0.146009989  0.257887425
## StateArkansas                                  -0.625065356 -0.516038962
## StateCalifornia                                -0.195801439 -0.062450464
## StateColorado                                  -0.120135673  0.002447472
## StateConnecticut                                0.089301661  0.222377470
## StateDelaware                                   0.020468319  0.155066167
## StateFlorida                                    0.294377706  0.412924559
## StateGeorgia                                    0.013906978  0.127609736
## StateHawaii                                    -0.608365093 -0.467150486
## StateIdaho                                     -0.275351996 -0.159066931
## StateIllinois                                   0.104812517  0.233581709
## StateIndiana                                   -0.023612076  0.076071921
## StateIowa                                      -0.732961003 -0.624312899
## StateKansas                                    -0.320955862 -0.224552743
## StateKentucky                                   0.592302264  0.686996193
## StateLouisiana                                  0.293469508  0.394888461
## StateMaine                                     -0.063869300  0.074857829
## StateMaryland                                  -1.672434093 -1.451851831
## StateMassachusetts                             -0.299079313 -0.083062578
## StateMichigan                                  -0.045169095  0.050576690
## StateMinnesota                                 -0.753441298 -0.645251331
## StateMississippi                               -0.209093790 -0.087268616
## StateMissouri                                   0.086401505  0.185702542
## StateMontana                                   -0.509216034 -0.394331541
## StateNebraska                                  -1.017176026 -0.912234589
## StateNevada                                     0.385989567  0.495672978
## StateNew Hampshire                              0.012195381  0.124591896
## StateNew Jersey                                -0.008620296  0.145727757
## StateNew Mexico                                 0.488774253  0.622210509
## StateNew York                                  -0.251050987 -0.132279799
## StateNorth Carolina                             0.187299971  0.274412387
## StateNorth Dakota                              -1.341397313 -1.172707883
## StateOhio                                       0.455678130  0.589151698
## StateOklahoma                                   0.337846240  0.453117480
## StateOregon                                    -0.415292220 -0.299059866
## StatePennsylvania                               0.561017187  0.677459526
## StateRhode Island                              -0.586170729 -0.312527565
## StateSouth Carolina                             0.046751608  0.161134027
## StateSouth Dakota                              -1.216535630 -1.084870928
## StateTennessee                                  0.383486326  0.470729691
## StateTexas                                     -0.032252917  0.087487525
## StateUtah                                      -0.238697614 -0.054041819
## StateVermont                                   -0.333329255 -0.191087648
## StateVirginia                                  -0.067956844  0.031405848
## StateWashington                                -0.095354561  0.024086450
## StateWest Virginia                              0.618242919  0.763862290
## StateWisconsin                                 -0.040024448  0.055350995
## StateWyoming                                   -0.156265025 -0.026862195
## Naloxone_Pharmacy_Yes_Redefined                -0.125945151 -0.061319716
## Naloxone_Pharmacy_No_Redefined                 -0.060956513  0.003373398
## Medical_Marijuana_Redefined                     0.129985765  0.199070518
## Recreational_Marijuana_Redefined               -0.174441233 -0.098626529
## GSL_Redefined                                   0.008441128  0.063283495
## PDMP_Redefined                                 -0.233796444 -0.178713621
## Medicaid_Expansion_Redefined                    0.038062580  0.089195898
## neg_2_pd                                       -0.090842524  0.020524738
## neg_3_pd                                       -0.093266935  0.016757110
## neg_4_pd                                       -0.130124958 -0.010783798
## neg_5_pd                                       -0.128729866 -0.013004948
## neg_6_pd                                       -0.115563431 -0.005778559
## neg_7_pd                                       -0.159146724 -0.044021509
## neg_8_pd                                       -0.243293082 -0.100544147
## neg_9_pd                                       -0.180033617 -0.025158944
## neg_10_pd                                      -0.117013914  0.024031356
## neg_11_pd                                      -0.123358860  0.025412131
## neg_12_pd                                      -0.047903816  0.115435529
## neg_13_pd                                      -0.150624459  0.015177292
## neg_14_pd                                      -0.172638404 -0.015729613
## neg_15_pd                                      -0.246143938 -0.059495317
## neg_16_pd                                      -0.215163327 -0.043767301
## neg_17_pd                                      -0.211202240 -0.060151411
## neg_18_pd                                      -0.194190577 -0.051908104
## neg_19_pd                                      -0.383178158 -0.154364075
## neg_20_pd                                      -0.446272143 -0.193711115
## neg_21_pd                                      -0.297364419 -0.117692721
## neg_22_pd                                      -0.284965743 -0.096423617
## neg_23_pd                                      -0.398786798 -0.116590871
## neg_24_pd                                      -0.517924064 -0.180864324
## neg_25_pd                                      -0.321229170 -0.038788957
## neg_26_pd                                      -0.301468962  0.044238456
## neg_27_pd                                      -0.707552430 -0.213628304
## neg_28_pd                                      -0.663134057 -0.201311333
## neg_29_pd                                      -0.241917565  0.024088229
## neg_30_pd                                      -0.304155495 -0.052096370
## neg_31_pd                                      -0.274766638 -0.054179201
## neg_32_pd                                      -0.177009269  0.032863102
## neg_33_pd                                      -0.212190787  0.109007659
## pos_0_pd                                       -0.117804387 -0.011149669
## pos_1_pd                                       -0.153952985 -0.040113963
## pos_2_pd                                       -0.109271024 -0.005207113
## pos_3_pd                                       -0.147951769 -0.041493922
## pos_4_pd                                       -0.153750936 -0.047126354
## pos_5_pd                                       -0.200386359 -0.092045551
## pos_6_pd                                       -0.210146623 -0.097121035
## pos_7_pd                                       -0.212953830 -0.094523821
## pos_8_pd                                       -0.253243669 -0.140578750
## pos_9_pd                                       -0.280162923 -0.162175014
## pos_10_pd                                      -0.305299298 -0.180016549
## pos_11_pd                                      -0.300854941 -0.183783467
## pos_12_pd                                      -0.316120292 -0.193795841
## pos_13_pd                                      -0.400921985 -0.262320233
## pos_14_pd                                      -0.386047681 -0.247335909
## pos_15_pd                                      -0.385495339 -0.250438341
## pos_16_pd                                      -0.408108802 -0.268524051
## pos_17_pd                                      -0.404219857 -0.263061724
## pos_18_pd                                      -0.398358676 -0.253663735
## pos_19_pd                                      -0.383498238 -0.243608362
## pos_20_pd                                      -0.396695074 -0.247582690
## pos_21_pd                                      -0.432711692 -0.274332431
## pos_22_pd                                      -0.422558279 -0.266749984
## pos_23_pd                                      -0.437700745 -0.273338184
## pos_24_pd                                      -0.485100733 -0.310854938
## pos_25_pd                                      -0.473288282 -0.279921074
## pos_26_pd                                      -0.478654088 -0.289983620
## pos_27_pd                                      -0.538577534 -0.338308822
## pos_28_pd                                      -0.527526463 -0.321207072
## pos_29_pd                                      -0.551613080 -0.334408979
## pos_30_pd                                      -0.510095934 -0.285008197
## pos_31_pd                                      -0.493354996 -0.241545861
## pos_32_pd                                      -0.545086726 -0.298666643
## pos_33_pd                                      -0.632136706 -0.326206090
## pos_34_pd                                      -0.629075408 -0.314276284
## pos_35_pd                                      -0.786883592 -0.514644392
## pos_36_pd                                      -0.801594573 -0.541250661
## pos_37_pd                                      -0.778573832 -0.534987709
## pos_38_pd                                      -0.752518722 -0.513830174
## pos_39_pd                                      -0.840631968 -0.534088308
## s(Time_Period_ID):as.factor(Region)Midwest.1   -0.604810921 -0.494737079
## s(Time_Period_ID):as.factor(Region)Midwest.2   -0.312013934 -0.224608521
## s(Time_Period_ID):as.factor(Region)Midwest.3    0.006447567  0.093175900
## s(Time_Period_ID):as.factor(Region)Midwest.4    0.248768267  0.333711394
## s(Time_Period_ID):as.factor(Region)Midwest.5    0.430895650  0.513087394
## s(Time_Period_ID):as.factor(Region)Midwest.6    0.614550129  0.703168971
## s(Time_Period_ID):as.factor(Region)Midwest.7    0.811163635  0.903771029
## s(Time_Period_ID):as.factor(Region)Midwest.8    1.041776231  1.159056321
## s(Time_Period_ID):as.factor(Region)Midwest.9    0.972590496  1.099762557
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.855128818 -0.570605352
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.575219298 -0.351951731
## s(Time_Period_ID):as.factor(Region)Northeast.3  0.137819821  0.305946250
## s(Time_Period_ID):as.factor(Region)Northeast.4  0.071834695  0.234789810
## s(Time_Period_ID):as.factor(Region)Northeast.5  0.186736401  0.353117285
## s(Time_Period_ID):as.factor(Region)Northeast.6  0.441019976  0.593323854
## s(Time_Period_ID):as.factor(Region)Northeast.7  0.824271871  0.987559759
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.248279088  1.424383187
## s(Time_Period_ID):as.factor(Region)Northeast.9  1.041444149  1.204455894
## s(Time_Period_ID):as.factor(Region)South.1     -0.485631359 -0.389922135
## s(Time_Period_ID):as.factor(Region)South.2     -0.207388443 -0.131694247
## s(Time_Period_ID):as.factor(Region)South.3      0.058850086  0.143187991
## s(Time_Period_ID):as.factor(Region)South.4      0.245225395  0.320084111
## s(Time_Period_ID):as.factor(Region)South.5      0.396570600  0.464161403
## s(Time_Period_ID):as.factor(Region)South.6      0.524700283  0.604633801
## s(Time_Period_ID):as.factor(Region)South.7      0.709248609  0.807908570
## s(Time_Period_ID):as.factor(Region)South.8      0.959164552  1.095942563
## s(Time_Period_ID):as.factor(Region)South.9      0.826912089  0.991245595
## s(Time_Period_ID):as.factor(Region)West.1      -0.427179482 -0.308386528
## s(Time_Period_ID):as.factor(Region)West.2      -0.223790527 -0.131400014
## s(Time_Period_ID):as.factor(Region)West.3      -0.020458926  0.069973226
## s(Time_Period_ID):as.factor(Region)West.4       0.155490954  0.230646763
## s(Time_Period_ID):as.factor(Region)West.5       0.276682349  0.357605994
## s(Time_Period_ID):as.factor(Region)West.6       0.375479806  0.468020533
## s(Time_Period_ID):as.factor(Region)West.7       0.468603452  0.566258884
## s(Time_Period_ID):as.factor(Region)West.8       0.603636187  0.719563215
## s(Time_Period_ID):as.factor(Region)West.9       0.586878298  0.704585511
##                                                      ub_coef    sd_coef
## (Intercept)                                    -9.4866868669 0.06176965
## StateAlaska                                     0.2508364222 0.07608223
## StateArizona                                    0.3697648601 0.05708032
## StateArkansas                                  -0.4070125673 0.05562571
## StateCalifornia                                 0.0709005101 0.06803621
## StateColorado                                   0.1250306159 0.06254242
## StateConnecticut                                0.3554532799 0.06789582
## StateDelaware                                   0.2896640143 0.06867237
## StateFlorida                                    0.5314714116 0.06048309
## StateGeorgia                                    0.2413124953 0.05801161
## StateHawaii                                    -0.3259358787 0.07204827
## StateIdaho                                     -0.0427818655 0.05932911
## StateIllinois                                   0.3623509004 0.06569857
## StateIndiana                                    0.1757559184 0.05085918
## StateIowa                                      -0.5156647960 0.05543271
## StateKansas                                    -0.1281496232 0.04918527
## StateKentucky                                   0.7816901223 0.04831323
## StateLouisiana                                  0.4963074142 0.05174436
## StateMaine                                      0.2135849575 0.07077915
## StateMaryland                                  -1.2312695688 0.11254197
## StateMassachusetts                              0.1329541565 0.11021262
## StateMichigan                                   0.1463224759 0.04884989
## StateMinnesota                                 -0.5370613641 0.05519896
## StateMississippi                                0.0345565579 0.06215570
## StateMissouri                                   0.2850035798 0.05066379
## StateMontana                                   -0.2794470485 0.05861454
## StateNebraska                                  -0.8072931523 0.05354155
## StateNevada                                     0.6053563884 0.05596092
## StateNew Hampshire                              0.2369884117 0.05734516
## StateNew Jersey                                 0.3000758093 0.07874901
## StateNew Mexico                                 0.7556467656 0.06807972
## StateNew York                                  -0.0135086105 0.06059754
## StateNorth Carolina                             0.3615248024 0.04444511
## StateNorth Dakota                              -1.0040184526 0.08606604
## StateOhio                                       0.7226252666 0.06809876
## StateOklahoma                                   0.5683887208 0.05881186
## StateOregon                                    -0.1828275119 0.05930222
## StatePennsylvania                               0.7939018648 0.05940936
## StateRhode Island                              -0.0388844005 0.13961386
## StateSouth Carolina                             0.2755164455 0.05835838
## StateSouth Dakota                              -0.9532062268 0.06717587
## StateTennessee                                  0.5579730566 0.04451192
## StateTexas                                      0.2072279669 0.06109206
## StateUtah                                       0.1306139757 0.09421214
## StateVermont                                   -0.0488460423 0.07257225
## StateVirginia                                   0.1307685399 0.05069525
## StateWashington                                 0.1435274614 0.06093929
## StateWest Virginia                              0.9094816603 0.07429560
## StateWisconsin                                  0.1507264367 0.04866094
## StateWyoming                                    0.1025406352 0.06602185
## Naloxone_Pharmacy_Yes_Redefined                 0.0033057204 0.03297216
## Naloxone_Pharmacy_No_Redefined                  0.0677033095 0.03282138
## Medical_Marijuana_Redefined                     0.2681552721 0.03524732
## Recreational_Marijuana_Redefined               -0.0228118260 0.03868097
## GSL_Redefined                                   0.1181258621 0.02798080
## PDMP_Redefined                                 -0.1236307979 0.02810348
## Medicaid_Expansion_Redefined                    0.1403292147 0.02608843
## neg_2_pd                                        0.1318919996 0.05682003
## neg_3_pd                                        0.1267811550 0.05613472
## neg_4_pd                                        0.1085573626 0.06088835
## neg_5_pd                                        0.1027199694 0.05904333
## neg_6_pd                                        0.1040063133 0.05601269
## neg_7_pd                                        0.0711037058 0.05873735
## neg_8_pd                                        0.0422047875 0.07283109
## neg_9_pd                                        0.1297157295 0.07901769
## neg_10_pd                                       0.1650766271 0.07196187
## neg_11_pd                                       0.1741831221 0.07590357
## neg_12_pd                                       0.2787748743 0.08333640
## neg_13_pd                                       0.1809790428 0.08459273
## neg_14_pd                                       0.1411791778 0.08005551
## neg_15_pd                                       0.1271533044 0.09522889
## neg_16_pd                                       0.1276287244 0.08744695
## neg_17_pd                                       0.0908994188 0.07706675
## neg_18_pd                                       0.0903743687 0.07259310
## neg_19_pd                                       0.0744500090 0.11674188
## neg_20_pd                                       0.0588499140 0.12885767
## neg_21_pd                                       0.0619789771 0.09166923
## neg_22_pd                                       0.0921185097 0.09619496
## neg_23_pd                                       0.1656050554 0.14397751
## neg_24_pd                                       0.1561954167 0.17196926
## neg_25_pd                                       0.2436512570 0.14410215
## neg_26_pd                                       0.3899458747 0.17638134
## neg_27_pd                                       0.2802958226 0.25200211
## neg_28_pd                                       0.2605113905 0.23562384
## neg_29_pd                                       0.2900940227 0.13571724
## neg_30_pd                                       0.1999627543 0.12860159
## neg_31_pd                                       0.1664082361 0.11254461
## neg_32_pd                                       0.2427354736 0.10707774
## neg_33_pd                                       0.4302061063 0.16387676
## pos_0_pd                                        0.0955050485 0.05441567
## pos_1_pd                                        0.0737250597 0.05808113
## pos_2_pd                                        0.0988567975 0.05309383
## pos_3_pd                                        0.0649639253 0.05431523
## pos_4_pd                                        0.0594982288 0.05440030
## pos_5_pd                                        0.0162952567 0.05527592
## pos_6_pd                                        0.0159045526 0.05766612
## pos_7_pd                                        0.0239061876 0.06042347
## pos_8_pd                                       -0.0279138306 0.05748210
## pos_9_pd                                       -0.0441871036 0.06019791
## pos_10_pd                                      -0.0547338000 0.06391977
## pos_11_pd                                      -0.0667119929 0.05973034
## pos_12_pd                                      -0.0714713887 0.06241043
## pos_13_pd                                      -0.1237184816 0.07071518
## pos_14_pd                                      -0.1086241379 0.07077131
## pos_15_pd                                      -0.1153813424 0.06890663
## pos_16_pd                                      -0.1289392991 0.07121671
## pos_17_pd                                      -0.1219035922 0.07201946
## pos_18_pd                                      -0.1089687946 0.07382395
## pos_19_pd                                      -0.1037184858 0.07137239
## pos_20_pd                                      -0.0984703060 0.07607775
## pos_21_pd                                      -0.1159531705 0.08080575
## pos_22_pd                                      -0.1109416884 0.07949403
## pos_23_pd                                      -0.1089756223 0.08385845
## pos_24_pd                                      -0.1366091424 0.08890092
## pos_25_pd                                      -0.0865538659 0.09865674
## pos_26_pd                                      -0.1013131529 0.09626044
## pos_27_pd                                      -0.1380401111 0.10217791
## pos_28_pd                                      -0.1148876812 0.10526500
## pos_29_pd                                      -0.1172048769 0.11081842
## pos_30_pd                                      -0.0599204594 0.11484068
## pos_31_pd                                       0.0102632731 0.12847405
## pos_32_pd                                      -0.0522465594 0.12572453
## pos_33_pd                                      -0.0202754733 0.15608705
## pos_34_pd                                       0.0005228401 0.16061180
## pos_35_pd                                      -0.2424051926 0.13889755
## pos_36_pd                                      -0.2809067482 0.13282853
## pos_37_pd                                      -0.2914015860 0.12427863
## pos_38_pd                                      -0.2751416257 0.12177987
## pos_39_pd                                      -0.2275446476 0.15639983
## s(Time_Period_ID):as.factor(Region)Midwest.1   -0.3846632372 0.05616012
## s(Time_Period_ID):as.factor(Region)Midwest.2   -0.1372031085 0.04459460
## s(Time_Period_ID):as.factor(Region)Midwest.3    0.1799042339 0.04424915
## s(Time_Period_ID):as.factor(Region)Midwest.4    0.4186545216 0.04333833
## s(Time_Period_ID):as.factor(Region)Midwest.5    0.5952791384 0.04193456
## s(Time_Period_ID):as.factor(Region)Midwest.6    0.7917878132 0.04521369
## s(Time_Period_ID):as.factor(Region)Midwest.7    0.9963784224 0.04724867
## s(Time_Period_ID):as.factor(Region)Midwest.8    1.2763364104 0.05983678
## s(Time_Period_ID):as.factor(Region)Midwest.9    1.2269346171 0.06488370
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.2860818865 0.14516503
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.1286841648 0.11391202
## s(Time_Period_ID):as.factor(Region)Northeast.3  0.4740726796 0.08577879
## s(Time_Period_ID):as.factor(Region)Northeast.4  0.3977449240 0.08314036
## s(Time_Period_ID):as.factor(Region)Northeast.5  0.5194981681 0.08488821
## s(Time_Period_ID):as.factor(Region)Northeast.6  0.7456277323 0.07770606
## s(Time_Period_ID):as.factor(Region)Northeast.7  1.1508476467 0.08331015
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.6004872852 0.08984903
## s(Time_Period_ID):as.factor(Region)Northeast.9  1.3674676378 0.08316926
## s(Time_Period_ID):as.factor(Region)South.1     -0.2942129097 0.04883124
## s(Time_Period_ID):as.factor(Region)South.2     -0.0560000507 0.03861949
## s(Time_Period_ID):as.factor(Region)South.3      0.2275258950 0.04302954
## s(Time_Period_ID):as.factor(Region)South.4      0.3949428261 0.03819322
## s(Time_Period_ID):as.factor(Region)South.5      0.5317522072 0.03448510
## s(Time_Period_ID):as.factor(Region)South.6      0.6845673191 0.04078241
## s(Time_Period_ID):as.factor(Region)South.7      0.9065685299 0.05033671
## s(Time_Period_ID):as.factor(Region)South.8      1.2327205728 0.06978470
## s(Time_Period_ID):as.factor(Region)South.9      1.1555791005 0.08384363
## s(Time_Period_ID):as.factor(Region)West.1      -0.1895935737 0.06060865
## s(Time_Period_ID):as.factor(Region)West.2      -0.0390095014 0.04713802
## s(Time_Period_ID):as.factor(Region)West.3       0.1604053778 0.04613885
## s(Time_Period_ID):as.factor(Region)West.4       0.3058025724 0.03834480
## s(Time_Period_ID):as.factor(Region)West.5       0.4385296390 0.04128757
## s(Time_Period_ID):as.factor(Region)West.6       0.5605612606 0.04721466
## s(Time_Period_ID):as.factor(Region)West.7       0.6639143157 0.04982420
## s(Time_Period_ID):as.factor(Region)West.8       0.8354902433 0.05914644
## s(Time_Period_ID):as.factor(Region)West.9       0.8222927245 0.06005470
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")

7.2.3 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_smoothed_time <- sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time %>%
  mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_log_smoothed_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_smoothed_time) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study_log_smoothed_time, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

7.2.4 Plot with Model SD

#compute the full dataset including basis functions
summary_model_log_smoothed <- summary(sensitivity_anlys_event_study_model_log_smoothed_time)
coef_values_log_smoothed <- data.frame(coef_values = coef(sensitivity_anlys_event_study_model_log_smoothed_time), 
                                       lb_coef = coef(sensitivity_anlys_event_study_model_log_smoothed_time) -
                                         1.96*summary_model_log_smoothed$se,
                                       ub_coef = coef(sensitivity_anlys_event_study_model_log_smoothed_time) +
                                         1.96*summary_model_log_smoothed$se,
                                       sd_coef = summary_model_log_smoothed$se)
#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_smoothed_time_sd_model <- coef_values_log_smoothed %>%
  mutate(term = rownames(coef_values_log_smoothed)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_smoothed_time_sd_model) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study_log_smoothed_time_sd_model, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

7.3 Analysis With Only Periods After Treatment

formula_post_tx_log_smoothed_time <- formula(paste("log(prop_dead)~ State +
                                           s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_smoothed_time<-gam(formula_post_tx_log_smoothed_time,
                                         data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_log_smoothed_time)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + pos_5_pd + 
##     pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + pos_11_pd + 
##     pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + pos_16_pd + 
##     pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + pos_21_pd + 
##     pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + pos_26_pd + 
##     pos_27_pd + pos_28_pd + pos_29_pd + pos_30_pd + pos_31_pd + 
##     pos_32_pd + pos_33_pd + pos_34_pd + pos_35_pd + pos_36_pd + 
##     pos_37_pd + pos_38_pd + pos_39_pd
## 
## Parametric coefficients:
##                                   Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -9.584292   0.054459 -175.991  < 2e-16 ***
## StateAlaska                       0.036666   0.075110    0.488 0.625491    
## StateArizona                      0.215228   0.067594    3.184 0.001476 ** 
## StateArkansas                    -0.548081   0.066435   -8.250 2.94e-16 ***
## StateCalifornia                  -0.026731   0.075894   -0.352 0.724716    
## StateColorado                    -0.035835   0.073958   -0.485 0.628062    
## StateConnecticut                  0.222839   0.070167    3.176 0.001518 ** 
## StateDelaware                     0.095876   0.068722    1.395 0.163144    
## StateFlorida                      0.456984   0.069492    6.576 6.24e-11 ***
## StateGeorgia                      0.179243   0.071084    2.522 0.011766 *  
## StateHawaii                      -0.499118   0.073830   -6.760 1.83e-11 ***
## StateIdaho                       -0.221927   0.067095   -3.308 0.000959 ***
## StateIllinois                     0.264387   0.068762    3.845 0.000125 ***
## StateIndiana                      0.055252   0.065747    0.840 0.400802    
## StateIowa                        -0.606608   0.066622   -9.105  < 2e-16 ***
## StateKansas                      -0.220016   0.065338   -3.367 0.000774 ***
## StateKentucky                     0.652366   0.066410    9.823  < 2e-16 ***
## StateLouisiana                    0.415581   0.066191    6.279 4.23e-10 ***
## StateMaine                        0.062938   0.073306    0.859 0.390685    
## StateMaryland                    -1.417519   0.068769  -20.613  < 2e-16 ***
## StateMassachusetts               -0.085762   0.066576   -1.288 0.197843    
## StateMichigan                     0.060031   0.068065    0.882 0.377908    
## StateMinnesota                   -0.642875   0.069185   -9.292  < 2e-16 ***
## StateMississippi                 -0.144053   0.066275   -2.174 0.029862 *  
## StateMissouri                     0.201635   0.067794    2.974 0.002974 ** 
## StateMontana                     -0.374776   0.070487   -5.317 1.18e-07 ***
## StateNebraska                    -0.953088   0.067064  -14.212  < 2e-16 ***
## StateNevada                       0.503141   0.071408    7.046 2.57e-12 ***
## StateNew Hampshire                0.105971   0.066600    1.591 0.111741    
## StateNew Jersey                   0.178806   0.068919    2.594 0.009548 ** 
## StateNew Mexico                   0.600453   0.072397    8.294  < 2e-16 ***
## StateNew York                    -0.130436   0.067618   -1.929 0.053881 .  
## StateNorth Carolina               0.288429   0.065582    4.398 1.15e-05 ***
## StateNorth Dakota                -1.215260   0.066417  -18.297  < 2e-16 ***
## StateOhio                         0.639643   0.071374    8.962  < 2e-16 ***
## StateOklahoma                     0.422230   0.065995    6.398 1.98e-10 ***
## StateOregon                      -0.315309   0.073339   -4.299 1.80e-05 ***
## StatePennsylvania                 0.719476   0.069683   10.325  < 2e-16 ***
## StateRhode Island                -0.371912   0.069540   -5.348 9.97e-08 ***
## StateSouth Carolina               0.099957   0.066880    1.495 0.135195    
## StateSouth Dakota                -1.143918   0.067494  -16.949  < 2e-16 ***
## StateTennessee                    0.470009   0.064906    7.241 6.44e-13 ***
## StateTexas                        0.126538   0.069110    1.831 0.067265 .  
## StateUtah                        -0.043458   0.065711   -0.661 0.508466    
## StateVermont                     -0.206642   0.069102   -2.990 0.002822 ** 
## StateVirginia                     0.056246   0.066538    0.845 0.398035    
## StateWashington                   0.016780   0.074571    0.225 0.821987    
## StateWest Virginia                0.719908   0.066663   10.799  < 2e-16 ***
## StateWisconsin                    0.076691   0.066321    1.156 0.247678    
## StateWyoming                     -0.040371   0.065371   -0.618 0.536929    
## Naloxone_Pharmacy_Yes_Redefined  -0.059310   0.042058   -1.410 0.158653    
## Naloxone_Pharmacy_No_Redefined    0.002961   0.038343    0.077 0.938448    
## Medical_Marijuana_Redefined       0.202801   0.030716    6.602 5.25e-11 ***
## Recreational_Marijuana_Redefined -0.093791   0.048565   -1.931 0.053606 .  
## GSL_Redefined                     0.063629   0.031447    2.023 0.043179 *  
## PDMP_Redefined                   -0.173420   0.024533   -7.069 2.19e-12 ***
## Medicaid_Expansion_Redefined      0.086304   0.030150    2.862 0.004250 ** 
## pos_0_pd                         -0.023324   0.045506   -0.513 0.608325    
## pos_1_pd                         -0.055506   0.046038   -1.206 0.228103    
## pos_2_pd                         -0.023570   0.046575   -0.506 0.612865    
## pos_3_pd                         -0.062660   0.047171   -1.328 0.184220    
## pos_4_pd                         -0.071229   0.047790   -1.490 0.136271    
## pos_5_pd                         -0.119086   0.048565   -2.452 0.014294 *  
## pos_6_pd                         -0.127267   0.049488   -2.572 0.010197 *  
## pos_7_pd                         -0.128092   0.050341   -2.544 0.011024 *  
## pos_8_pd                         -0.177959   0.051778   -3.437 0.000601 ***
## pos_9_pd                         -0.203349   0.052920   -3.843 0.000126 ***
## pos_10_pd                        -0.224738   0.053667   -4.188 2.95e-05 ***
## pos_11_pd                        -0.232286   0.054842   -4.236 2.39e-05 ***
## pos_12_pd                        -0.246048   0.056058   -4.389 1.20e-05 ***
## pos_13_pd                        -0.318017   0.056913   -5.588 2.64e-08 ***
## pos_14_pd                        -0.306890   0.059028   -5.199 2.22e-07 ***
## pos_15_pd                        -0.313919   0.060466   -5.192 2.31e-07 ***
## pos_16_pd                        -0.335444   0.061495   -5.455 5.55e-08 ***
## pos_17_pd                        -0.333681   0.063816   -5.229 1.90e-07 ***
## pos_18_pd                        -0.327594   0.065387   -5.010 5.95e-07 ***
## pos_19_pd                        -0.320472   0.066387   -4.827 1.50e-06 ***
## pos_20_pd                        -0.328184   0.069238   -4.740 2.30e-06 ***
## pos_21_pd                        -0.358287   0.072135   -4.967 7.42e-07 ***
## pos_22_pd                        -0.354073   0.073901   -4.791 1.79e-06 ***
## pos_23_pd                        -0.364271   0.076024   -4.792 1.79e-06 ***
## pos_24_pd                        -0.403976   0.080816   -4.999 6.31e-07 ***
## pos_25_pd                        -0.375638   0.085341   -4.402 1.13e-05 ***
## pos_26_pd                        -0.388972   0.086291   -4.508 6.96e-06 ***
## pos_27_pd                        -0.440989   0.087485   -5.041 5.08e-07 ***
## pos_28_pd                        -0.426885   0.088804   -4.807 1.65e-06 ***
## pos_29_pd                        -0.443487   0.096615   -4.590 4.72e-06 ***
## pos_30_pd                        -0.397226   0.099775   -3.981 7.12e-05 ***
## pos_31_pd                        -0.358305   0.103237   -3.471 0.000531 ***
## pos_32_pd                        -0.419854   0.113771   -3.690 0.000230 ***
## pos_33_pd                        -0.451055   0.118929   -3.793 0.000154 ***
## pos_34_pd                        -0.442611   0.120199   -3.682 0.000238 ***
## pos_35_pd                        -0.646812   0.139615   -4.633 3.85e-06 ***
## pos_36_pd                        -0.677019   0.140997   -4.802 1.70e-06 ***
## pos_37_pd                        -0.675026   0.166873   -4.045 5.44e-05 ***
## pos_38_pd                        -0.656919   0.222706   -2.950 0.003220 ** 
## pos_39_pd                        -0.680624   0.224519   -3.031 0.002467 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df      F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   4.455  5.471 153.62  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.455  8.915  90.67  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     5.852  7.002 117.40  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      3.088  3.868 112.48  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.844   Deviance explained = 85.3%
## GCV = 0.089287  Scale est. = 0.083981  n = 2000

7.3.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time <-
  data.frame(predict(sensitivity_anlys_post_tx_model_log_smoothed_time, type = "lpmatrix"))

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time <- coef(sensitivity_anlys_post_tx_model_log_smoothed_time)

sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time <- 
  compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time), 
                    log(sensitivity_anlys_event_study_data$prop_dead),
                    coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time, 
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time
##                                                      lb_coef  coef_values
## (Intercept)                                    -9.6854539768 -9.584291850
## StateAlaska                                    -0.1046639660  0.036665976
## StateArizona                                    0.1089977014  0.215227642
## StateArkansas                                  -0.6564095521 -0.548081195
## StateCalifornia                                -0.1545483250 -0.026730935
## StateColorado                                  -0.1541190275 -0.035835468
## StateConnecticut                                0.0891506296  0.222839006
## StateDelaware                                  -0.0324643342  0.095876016
## StateFlorida                                    0.3509994555  0.456983881
## StateGeorgia                                    0.0815691356  0.179243421
## StateHawaii                                    -0.6267861328 -0.499117982
## StateIdaho                                     -0.3216318260 -0.221926721
## StateIllinois                                   0.1400446967  0.264386589
## StateIndiana                                   -0.0438355817  0.055252347
## StateIowa                                      -0.7106638951 -0.606607774
## StateKansas                                    -0.3152093450 -0.220016045
## StateKentucky                                   0.5640805615  0.652366107
## StateLouisiana                                  0.3200969306  0.415580961
## StateMaine                                     -0.0741560744  0.062938240
## StateMaryland                                  -1.6271647021 -1.417519222
## StateMassachusetts                             -0.2978866868 -0.085761822
## StateMichigan                                  -0.0328569759  0.060031010
## StateMinnesota                                 -0.7482847354 -0.642874783
## StateMississippi                               -0.2529389837 -0.144052614
## StateMissouri                                   0.1111016167  0.201635194
## StateMontana                                   -0.4841245915 -0.374776251
## StateNebraska                                  -1.0504079937 -0.953088399
## StateNevada                                     0.3948210378  0.503141396
## StateNew Hampshire                             -0.0070535739  0.105971146
## StateNew Jersey                                 0.0294406824  0.178806146
## StateNew Mexico                                 0.4703653251  0.600453346
## StateNew York                                  -0.2486903177 -0.130435518
## StateNorth Carolina                             0.2076694369  0.288428714
## StateNorth Dakota                              -1.3778197767 -1.215260174
## StateOhio                                       0.5159235266  0.639642699
## StateOklahoma                                   0.3118844528  0.422229947
## StateOregon                                    -0.4297868703 -0.315309225
## StatePennsylvania                               0.6084660641  0.719475961
## StateRhode Island                              -0.6688200051 -0.371911783
## StateSouth Carolina                             0.0018107169  0.099957021
## StateSouth Dakota                              -1.2718479943 -1.143917518
## StateTennessee                                  0.3877071260  0.470009368
## StateTexas                                      0.0119858424  0.126537743
## StateUtah                                      -0.2247810111 -0.043458216
## StateVermont                                   -0.3498881414 -0.206641925
## StateVirginia                                  -0.0376742496  0.056246365
## StateWashington                                -0.1006345297  0.016780005
## StateWest Virginia                              0.5796552871  0.719907762
## StateWisconsin                                 -0.0098912006  0.076691456
## StateWyoming                                   -0.1684715652 -0.040371406
## Naloxone_Pharmacy_Yes_Redefined                -0.1232720216 -0.059309662
## Naloxone_Pharmacy_No_Redefined                 -0.0611427875  0.002961323
## Medical_Marijuana_Redefined                     0.1330887661  0.202800700
## Recreational_Marijuana_Redefined               -0.1666378312 -0.093790626
## GSL_Redefined                                   0.0097162405  0.063628690
## PDMP_Redefined                                 -0.2268263907 -0.173420410
## Medicaid_Expansion_Redefined                    0.0350389201  0.086304415
## pos_0_pd                                       -0.1024720232 -0.023324068
## pos_1_pd                                       -0.1451126027 -0.055506248
## pos_2_pd                                       -0.1004104047 -0.023570479
## pos_3_pd                                       -0.1414234174 -0.062659755
## pos_4_pd                                       -0.1492366487 -0.071228602
## pos_5_pd                                       -0.1998057945 -0.119086036
## pos_6_pd                                       -0.2139031025 -0.127267389
## pos_7_pd                                       -0.2212403506 -0.128091984
## pos_8_pd                                       -0.2645405128 -0.177959284
## pos_9_pd                                       -0.2965781987 -0.203348513
## pos_10_pd                                      -0.3270500612 -0.224738242
## pos_11_pd                                      -0.3244860166 -0.232285551
## pos_12_pd                                      -0.3455443752 -0.246047943
## pos_13_pd                                      -0.4356205193 -0.318017387
## pos_14_pd                                      -0.4248015800 -0.306890154
## pos_15_pd                                      -0.4261722901 -0.313919283
## pos_16_pd                                      -0.4534278872 -0.335444166
## pos_17_pd                                      -0.4527739444 -0.333680862
## pos_18_pd                                      -0.4491299493 -0.327593795
## pos_19_pd                                      -0.4358931487 -0.320472170
## pos_20_pd                                      -0.4530153148 -0.328184413
## pos_21_pd                                      -0.4934693511 -0.358286616
## pos_22_pd                                      -0.4870884590 -0.354073454
## pos_23_pd                                      -0.5046859006 -0.364270946
## pos_24_pd                                      -0.5539080092 -0.403976112
## pos_25_pd                                      -0.5461140217 -0.375638035
## pos_26_pd                                      -0.5556522361 -0.388971914
## pos_27_pd                                      -0.6207396652 -0.440988642
## pos_28_pd                                      -0.6134503770 -0.426885256
## pos_29_pd                                      -0.6408056504 -0.443487315
## pos_30_pd                                      -0.6024869638 -0.397225581
## pos_31_pd                                      -0.5910035924 -0.358304832
## pos_32_pd                                      -0.6438075396 -0.419853706
## pos_33_pd                                      -0.7387147151 -0.451055372
## pos_34_pd                                      -0.7393531460 -0.442610508
## pos_35_pd                                      -0.8957024262 -0.646811613
## pos_36_pd                                      -0.9116379639 -0.677018978
## pos_37_pd                                      -0.8933535869 -0.675025871
## pos_38_pd                                      -0.8670115452 -0.656919440
## pos_39_pd                                      -0.9658711335 -0.680623994
## s(Time_Period_ID):as.factor(Region)Midwest.1   -0.6326139695 -0.529045004
## s(Time_Period_ID):as.factor(Region)Midwest.2   -0.3390176169 -0.249784199
## s(Time_Period_ID):as.factor(Region)Midwest.3    0.0007546299  0.087068355
## s(Time_Period_ID):as.factor(Region)Midwest.4    0.2573746884  0.343106203
## s(Time_Period_ID):as.factor(Region)Midwest.5    0.4489039132  0.535484239
## s(Time_Period_ID):as.factor(Region)Midwest.6    0.6477021289  0.738911416
## s(Time_Period_ID):as.factor(Region)Midwest.7    0.8641835303  0.954608869
## s(Time_Period_ID):as.factor(Region)Midwest.8    1.1137572711  1.226978851
## s(Time_Period_ID):as.factor(Region)Midwest.9    1.0496931478  1.168645122
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.8497237979 -0.555935063
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.5965035114 -0.369120947
## s(Time_Period_ID):as.factor(Region)Northeast.3  0.1420908472  0.314673088
## s(Time_Period_ID):as.factor(Region)Northeast.4  0.0941825739  0.261684737
## s(Time_Period_ID):as.factor(Region)Northeast.5  0.2137588935  0.386082047
## s(Time_Period_ID):as.factor(Region)Northeast.6  0.4862851444  0.644137155
## s(Time_Period_ID):as.factor(Region)Northeast.7  0.8809900634  1.049465437
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.3262754392  1.506472200
## s(Time_Period_ID):as.factor(Region)Northeast.9  1.1173502743  1.280813198
## s(Time_Period_ID):as.factor(Region)South.1     -0.5120365474 -0.429299322
## s(Time_Period_ID):as.factor(Region)South.2     -0.2278641820 -0.156629395
## s(Time_Period_ID):as.factor(Region)South.3      0.0571040728  0.137467348
## s(Time_Period_ID):as.factor(Region)South.4      0.2593436573  0.333216002
## s(Time_Period_ID):as.factor(Region)South.5      0.4287657460  0.492053009
## s(Time_Period_ID):as.factor(Region)South.6      0.5691752517  0.643346729
## s(Time_Period_ID):as.factor(Region)South.7      0.7721608305  0.859875036
## s(Time_Period_ID):as.factor(Region)South.8      1.0412564197  1.162306774
## s(Time_Period_ID):as.factor(Region)South.9      0.9150235656  1.066395234
## s(Time_Period_ID):as.factor(Region)West.1      -0.4481931667 -0.336007136
## s(Time_Period_ID):as.factor(Region)West.2      -0.2307383682 -0.145013221
## s(Time_Period_ID):as.factor(Region)West.3      -0.0138080998  0.072013723
## s(Time_Period_ID):as.factor(Region)West.4       0.1761311647  0.247261807
## s(Time_Period_ID):as.factor(Region)West.5       0.3125934745  0.386821789
## s(Time_Period_ID):as.factor(Region)West.6       0.4208680316  0.508678919
## s(Time_Period_ID):as.factor(Region)West.7       0.5214461873  0.618216906
## s(Time_Period_ID):as.factor(Region)West.8       0.6702804526  0.787663851
## s(Time_Period_ID):as.factor(Region)West.9       0.6624388979  0.774066969
##                                                     ub_coef    sd_coef
## (Intercept)                                    -9.483129723 0.05161333
## StateAlaska                                     0.177995918 0.07210711
## StateArizona                                    0.321457582 0.05419895
## StateArkansas                                  -0.439752837 0.05526957
## StateCalifornia                                 0.101086456 0.06521295
## StateColorado                                   0.082448092 0.06034875
## StateConnecticut                                0.356527382 0.06820836
## StateDelaware                                   0.224216366 0.06547977
## StateFlorida                                    0.562968307 0.05407369
## StateGeorgia                                    0.276917707 0.04983382
## StateHawaii                                    -0.371449832 0.06513681
## StateIdaho                                     -0.122221617 0.05086995
## StateIllinois                                   0.388728482 0.06343974
## StateIndiana                                    0.154340276 0.05055507
## StateIowa                                      -0.502551654 0.05308986
## StateKansas                                    -0.124822744 0.04856801
## StateKentucky                                   0.740651653 0.04504365
## StateLouisiana                                  0.511064992 0.04871634
## StateMaine                                      0.200032554 0.06994608
## StateMaryland                                  -1.207873742 0.10696198
## StateMassachusetts                              0.126363042 0.10822697
## StateMichigan                                   0.152918996 0.04739183
## StateMinnesota                                 -0.537464831 0.05378059
## StateMississippi                               -0.035166245 0.05555427
## StateMissouri                                   0.292168772 0.04619060
## StateMontana                                   -0.265427911 0.05578997
## StateNebraska                                  -0.855768805 0.04965285
## StateNevada                                     0.611461754 0.05526549
## StateNew Hampshire                              0.218995866 0.05766567
## StateNew Jersey                                 0.328171610 0.07620687
## StateNew Mexico                                 0.730541367 0.06637144
## StateNew York                                  -0.012180719 0.06033408
## StateNorth Carolina                             0.369187991 0.04120371
## StateNorth Dakota                              -1.052700571 0.08293857
## StateOhio                                       0.763361871 0.06312203
## StateOklahoma                                   0.532575442 0.05629872
## StateOregon                                    -0.200831581 0.05840696
## StatePennsylvania                               0.830485859 0.05663770
## StateRhode Island                              -0.075003561 0.15148379
## StateSouth Carolina                             0.198103326 0.05007465
## StateSouth Dakota                              -1.015987042 0.06527065
## StateTennessee                                  0.552311609 0.04199094
## StateTexas                                      0.241089643 0.05844485
## StateUtah                                       0.137864579 0.09251163
## StateVermont                                   -0.063395708 0.07308480
## StateVirginia                                   0.150166979 0.04791868
## StateWashington                                 0.134194539 0.05990537
## StateWest Virginia                              0.860160238 0.07155739
## StateWisconsin                                  0.163274112 0.04417482
## StateWyoming                                    0.087728753 0.06535722
## Naloxone_Pharmacy_Yes_Redefined                 0.004652698 0.03263386
## Naloxone_Pharmacy_No_Redefined                  0.067065434 0.03270618
## Medical_Marijuana_Redefined                     0.272512634 0.03556731
## Recreational_Marijuana_Redefined               -0.020943422 0.03716694
## GSL_Redefined                                   0.117541140 0.02750635
## PDMP_Redefined                                 -0.120014429 0.02724795
## Medicaid_Expansion_Redefined                    0.137569911 0.02615586
## pos_0_pd                                        0.055823888 0.04038161
## pos_1_pd                                        0.034100107 0.04571753
## pos_2_pd                                        0.053269448 0.03920404
## pos_3_pd                                        0.016103908 0.04018554
## pos_4_pd                                        0.006779444 0.03980002
## pos_5_pd                                       -0.038366277 0.04118355
## pos_6_pd                                       -0.040631676 0.04420189
## pos_7_pd                                       -0.034943618 0.04752468
## pos_8_pd                                       -0.091378056 0.04417410
## pos_9_pd                                       -0.110118826 0.04756617
## pos_10_pd                                      -0.122426422 0.05219991
## pos_11_pd                                      -0.140085085 0.04704105
## pos_12_pd                                      -0.146551510 0.05076349
## pos_13_pd                                      -0.200414254 0.06000160
## pos_14_pd                                      -0.188978728 0.06015889
## pos_15_pd                                      -0.201666277 0.05727194
## pos_16_pd                                      -0.217460445 0.06019578
## pos_17_pd                                      -0.214587779 0.06076178
## pos_18_pd                                      -0.206057640 0.06200824
## pos_19_pd                                      -0.205051190 0.05888825
## pos_20_pd                                      -0.203353512 0.06368924
## pos_21_pd                                      -0.223103881 0.06897078
## pos_22_pd                                      -0.221058450 0.06786480
## pos_23_pd                                      -0.223855991 0.07164028
## pos_24_pd                                      -0.254044215 0.07649587
## pos_25_pd                                      -0.205162049 0.08697754
## pos_26_pd                                      -0.222291592 0.08504098
## pos_27_pd                                      -0.261237619 0.09170971
## pos_28_pd                                      -0.240320136 0.09518629
## pos_29_pd                                      -0.246168980 0.10067262
## pos_30_pd                                      -0.191964198 0.10472520
## pos_31_pd                                      -0.125606072 0.11872386
## pos_32_pd                                      -0.195899872 0.11426216
## pos_33_pd                                      -0.163396029 0.14676497
## pos_34_pd                                      -0.145867869 0.15139931
## pos_35_pd                                      -0.397920801 0.12698511
## pos_36_pd                                      -0.442399992 0.11970356
## pos_37_pd                                      -0.456698155 0.11139169
## pos_38_pd                                      -0.446827335 0.10718985
## pos_39_pd                                      -0.395376855 0.14553425
## s(Time_Period_ID):as.factor(Region)Midwest.1   -0.425476039 0.05284131
## s(Time_Period_ID):as.factor(Region)Midwest.2   -0.160550780 0.04552725
## s(Time_Period_ID):as.factor(Region)Midwest.3    0.173382079 0.04403761
## s(Time_Period_ID):as.factor(Region)Midwest.4    0.428837717 0.04374057
## s(Time_Period_ID):as.factor(Region)Midwest.5    0.622064564 0.04417364
## s(Time_Period_ID):as.factor(Region)Midwest.6    0.830120702 0.04653535
## s(Time_Period_ID):as.factor(Region)Midwest.7    1.045034207 0.04613538
## s(Time_Period_ID):as.factor(Region)Midwest.8    1.340200431 0.05776611
## s(Time_Period_ID):as.factor(Region)Midwest.9    1.287597097 0.06068978
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.262146329 0.14989221
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.141738382 0.11601151
## s(Time_Period_ID):as.factor(Region)Northeast.3  0.487255330 0.08805216
## s(Time_Period_ID):as.factor(Region)Northeast.4  0.429186901 0.08546029
## s(Time_Period_ID):as.factor(Region)Northeast.5  0.558405201 0.08791998
## s(Time_Period_ID):as.factor(Region)Northeast.6  0.801989165 0.08053674
## s(Time_Period_ID):as.factor(Region)Northeast.7  1.217940811 0.08595682
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.686668961 0.09193712
## s(Time_Period_ID):as.factor(Region)Northeast.9  1.444276122 0.08339945
## s(Time_Period_ID):as.factor(Region)South.1     -0.346562096 0.04221287
## s(Time_Period_ID):as.factor(Region)South.2     -0.085394608 0.03634428
## s(Time_Period_ID):as.factor(Region)South.3      0.217830622 0.04100167
## s(Time_Period_ID):as.factor(Region)South.4      0.407088346 0.03768997
## s(Time_Period_ID):as.factor(Region)South.5      0.555340273 0.03228942
## s(Time_Period_ID):as.factor(Region)South.6      0.717518207 0.03784259
## s(Time_Period_ID):as.factor(Region)South.7      0.947589242 0.04475215
## s(Time_Period_ID):as.factor(Region)South.8      1.283357129 0.06176039
## s(Time_Period_ID):as.factor(Region)South.9      1.217766902 0.07723044
## s(Time_Period_ID):as.factor(Region)West.1      -0.223821106 0.05723777
## s(Time_Period_ID):as.factor(Region)West.2      -0.059288074 0.04373732
## s(Time_Period_ID):as.factor(Region)West.3       0.157835545 0.04378664
## s(Time_Period_ID):as.factor(Region)West.4       0.318392450 0.03629114
## s(Time_Period_ID):as.factor(Region)West.5       0.461050104 0.03787159
## s(Time_Period_ID):as.factor(Region)West.6       0.596489806 0.04480147
## s(Time_Period_ID):as.factor(Region)West.7       0.714987624 0.04937282
## s(Time_Period_ID):as.factor(Region)West.8       0.905047249 0.05988949
## s(Time_Period_ID):as.factor(Region)West.9       0.885695041 0.05695310

7.3.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_smoothed_time <- sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_smoothed_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_smoothed_time$num_states <- sapply(plot_post_tx_log_smoothed_time$term,
                                                    function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx_log_smoothed_time, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() 

  # geom_vline(aes(xintercept = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
  # geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), y = 12, 
  #           x = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"] + 0.1), color = "red")
  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

7.3.3 Attributable Deaths

date_data <- sensitivity_anlys_event_study_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_smoothed_time_post_tx <- attr_death_compute(sensitivity_anlys_event_study_data,
                                                                sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time)
attr_deaths_est_log_smoothed_time_post_tx <- merge(attr_deaths_est_log_smoothed_time_post_tx, date_data, 
                                               by.x = "Time_Period", by.y = "Time_Period_ID")

ggplot(attr_deaths_est_log_smoothed_time_post_tx, aes(x = Time_Period_Start)) + 
  # geom_point(aes(y = attr_deaths)) + 
  geom_line(aes(y = attr_deaths, linetype = "Estimate")) + 
  # geom_point(aes(y = attr_deaths_lb)) + 
  geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) + 
  # geom_point(aes(y = attr_deaths_ub)) + 
  geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) + 
  labs(x = "Date", y = "Attributable Deaths",
       title = "Estimated Number of Attributable Deaths Using Semi-Dynamic Model",
       linetype = "") + 
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black")) + 
  scale_linetype_manual(values = c("dashed", "solid"))

7.3.4 Model With Semi Dynamic Regression

coef_semi_dynamic <- data.frame(matrix(NA, nrow = 40, ncol = 4))
for(time in 0:39){
  subset_data <- sensitivity_anlys_event_study_data %>%
    filter(get(paste("pos_", time, "_pd", sep = "")) == 1 | 
             Time_Period_Start <= Intervention_First_Date)
  formula_semi_dynamic <- formula(paste("log(prop_dead)~ State +
                                           s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                        paste("pos_", time, "_pd", sep = "")))
  #run the gam model
  semi_dynamic_model<-gam(formula_semi_dynamic, data = subset_data)
  summary_semi_dynamic_model <- summary(semi_dynamic_model)
  sd_semi_dynamic_model <- summary_semi_dynamic_model$se[paste("pos_", time, "_pd", sep = "")]
  
  coef_value <- coef(semi_dynamic_model)[paste("pos_", time, "_pd", sep = "")]
  
  coef_semi_dynamic[time + 1,] <- c(time, coef_value, coef_value - 1.96*sd_semi_dynamic_model, coef_value + 1.96*sd_semi_dynamic_model)
}

colnames(coef_semi_dynamic) <- c("time_after_tx", "estimate", "lb", "ub")

ggplot(coef_semi_dynamic, aes(y = estimate, x = time_after_tx)) + 
  geom_pointrange(aes(ymin = lb, ymax = ub), fatten = 1)

7.4 Analysis With Only Periods After Treatment with Model SD

summary_model_log_smoothed_post_tx <- summary(sensitivity_anlys_post_tx_model_log_smoothed_time)
coef_values_log_smoothed_post_tx <- data.frame(coef_values = coef(sensitivity_anlys_post_tx_model_log_smoothed_time), 
                                       lb_coef = coef(sensitivity_anlys_post_tx_model_log_smoothed_time) -
                                         1.96*summary_model_log_smoothed_post_tx$se,
                                       ub_coef = coef(sensitivity_anlys_post_tx_model_log_smoothed_time) +
                                         1.96*summary_model_log_smoothed_post_tx$se,
                                       sd_coef = summary_model_log_smoothed_post_tx$se)

7.4.1 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_smoothed_time_post_tx <- coef_values_log_smoothed_post_tx %>%
  mutate(term = rownames(coef_values_log_smoothed_post_tx)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_smoothed_time_post_tx) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_smoothed_time_post_tx$num_states <- sapply(plot_post_tx_log_smoothed_time_post_tx$term,
                                                    function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx_log_smoothed_time_post_tx, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_vline(aes(xintercept = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
  geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), y = 12, 
            x = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"] + 0.1), color = "red")

  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

7.5 Analysis With Linear Periods After Treatment

#use this function to compute the cumulative sum, but resets the sum if the variable was 0
compute_cumsum = function(x){
    cs = cumsum(x)
    cs - cummax((x == 0) * cs)
}
sensitivity_anlys_event_study_data_lin_post_tx <- sensitivity_anlys_event_study_data %>%
  arrange(State, Time_Period_ID) %>%
  group_by(State) %>%
  mutate(sum_tx_periods = pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + 
           pos_4_pd + pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + 
           pos_10_pd + pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd + 
           pos_15_pd + pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd + 
           pos_20_pd + pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd + 
           pos_25_pd + pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd + 
           pos_30_pd + pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd + 
           pos_35_pd + pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd,
         time_after_tx = cumsum(sum_tx_periods),
         num_pd_w_tx = compute_cumsum(Intervention_Redefined ),
         num_pd_w_naloxone_yes = compute_cumsum(Naloxone_Pharmacy_Yes_Redefined),
         num_pd_w_naloxone_no = compute_cumsum(Naloxone_Pharmacy_No_Redefined),
         num_pd_w_med_marijuana = compute_cumsum(Medical_Marijuana_Redefined),
         num_pd_w_rec_marijuana = compute_cumsum(Recreational_Marijuana_Redefined),
         num_pd_w_gsl = compute_cumsum(GSL_Redefined),
         num_pd_w_pdmp = compute_cumsum(PDMP_Redefined),
         num_pd_w_medicaid = compute_cumsum(Medicaid_Expansion_Redefined),
         lag_num_pd_w_tx = lag(num_pd_w_tx)) #lag so that intercept = effect when tx first occurs

#fill in a 0 for the NAs so we keep all the data and at most this will be 0
sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx[is.na(sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx)] <- 0

#run the gam model
sensitivity_anlys_lin_post_tx_model_log_smoothed_time<-gam(log(prop_dead)~ State +
                                                             s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                                             num_pd_w_naloxone_yes +
                                                             num_pd_w_naloxone_no +
                                                             num_pd_w_med_marijuana +
                                                             num_pd_w_rec_marijuana +
                                                             num_pd_w_gsl +
                                                             num_pd_w_pdmp +
                                                             num_pd_w_medicaid +
                                                             Intervention_Redefined +
                                                             lag_num_pd_w_tx,
                                                           data = sensitivity_anlys_event_study_data_lin_post_tx)
summary(sensitivity_anlys_lin_post_tx_model_log_smoothed_time)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     num_pd_w_naloxone_yes + num_pd_w_naloxone_no + num_pd_w_med_marijuana + 
##     num_pd_w_rec_marijuana + num_pd_w_gsl + num_pd_w_pdmp + num_pd_w_medicaid + 
##     Intervention_Redefined + lag_num_pd_w_tx
## 
## Parametric coefficients:
##                          Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)            -9.8183490  0.0556256 -176.508  < 2e-16 ***
## StateAlaska             0.4171746  0.0802721    5.197 2.24e-07 ***
## StateArizona            0.3760830  0.0670104    5.612 2.29e-08 ***
## StateArkansas          -0.4059470  0.0678565   -5.982 2.62e-09 ***
## StateCalifornia         0.1638949  0.0827625    1.980 0.047812 *  
## StateColorado           0.3024756  0.0756626    3.998 6.64e-05 ***
## StateConnecticut        0.3454200  0.0727701    4.747 2.22e-06 ***
## StateDelaware           0.3161505  0.0688666    4.591 4.70e-06 ***
## StateFlorida            0.5664793  0.0701076    8.080 1.13e-15 ***
## StateGeorgia            0.3153556  0.0718656    4.388 1.21e-05 ***
## StateHawaii            -0.3147575  0.0821161   -3.833 0.000131 ***
## StateIdaho             -0.3507383  0.0699840   -5.012 5.89e-07 ***
## StateIllinois           0.2758364  0.0729175    3.783 0.000160 ***
## StateIndiana           -0.1025759  0.0686310   -1.495 0.135183    
## StateIowa              -0.6002178  0.0666147   -9.010  < 2e-16 ***
## StateKansas            -0.1640845  0.0658173   -2.493 0.012749 *  
## StateKentucky           0.5163621  0.0690509    7.478 1.14e-13 ***
## StateLouisiana          0.4502306  0.0662037    6.801 1.39e-11 ***
## StateMaine              0.3826328  0.0789499    4.847 1.36e-06 ***
## StateMaryland          -1.2575835  0.0707303  -17.780  < 2e-16 ***
## StateMassachusetts     -0.1576709  0.0687445   -2.294 0.021922 *  
## StateMichigan           0.0580381  0.0706337    0.822 0.411362    
## StateMinnesota         -0.4026034  0.0705033   -5.710 1.30e-08 ***
## StateMississippi       -0.1421124  0.0662557   -2.145 0.032086 *  
## StateMissouri           0.4574842  0.0700174    6.534 8.19e-11 ***
## StateMontana           -0.0003051  0.0725785   -0.004 0.996646    
## StateNebraska          -0.8175986  0.0677976  -12.059  < 2e-16 ***
## StateNevada             0.6546011  0.0775381    8.442  < 2e-16 ***
## StateNew Hampshire      0.3207231  0.0679253    4.722 2.51e-06 ***
## StateNew Jersey         0.3458793  0.0693044    4.991 6.56e-07 ***
## StateNew Mexico         0.7922907  0.0784424   10.100  < 2e-16 ***
## StateNew York          -0.1990437  0.0699730   -2.845 0.004494 ** 
## StateNorth Carolina     0.3142558  0.0659779    4.763 2.05e-06 ***
## StateNorth Dakota      -1.1760400  0.0663083  -17.736  < 2e-16 ***
## StateOhio               0.6677233  0.0704338    9.480  < 2e-16 ***
## StateOklahoma           0.3057100  0.0686792    4.451 9.03e-06 ***
## StateOregon             0.1541645  0.0775496    1.988 0.046960 *  
## StatePennsylvania       0.6210185  0.0718327    8.645  < 2e-16 ***
## StateRhode Island      -0.2827495  0.0723100   -3.910 9.54e-05 ***
## StateSouth Carolina     0.1340333  0.0668806    2.004 0.045203 *  
## StateSouth Dakota      -1.0307736  0.0683303  -15.085  < 2e-16 ***
## StateTennessee          0.4235722  0.0655056    6.466 1.27e-10 ***
## StateTexas             -0.0059759  0.0713798   -0.084 0.933288    
## StateUtah              -0.1801834  0.0690426   -2.610 0.009132 ** 
## StateVermont            0.0681485  0.0695052    0.980 0.326972    
## StateVirginia          -0.0067563  0.0672381   -0.100 0.919971    
## StateWashington         0.3781016  0.0768966    4.917 9.54e-07 ***
## StateWest Virginia      0.5864998  0.0697456    8.409  < 2e-16 ***
## StateWisconsin          0.1798570  0.0673732    2.670 0.007659 ** 
## StateWyoming           -0.1055152  0.0657774   -1.604 0.108851    
## num_pd_w_naloxone_yes  -0.0274867  0.0064854   -4.238 2.36e-05 ***
## num_pd_w_naloxone_no   -0.0118751  0.0036375   -3.265 0.001115 ** 
## num_pd_w_med_marijuana -0.0077139  0.0021669   -3.560 0.000380 ***
## num_pd_w_rec_marijuana -0.0231385  0.0080380   -2.879 0.004038 ** 
## num_pd_w_gsl            0.0148938  0.0037555    3.966 7.58e-05 ***
## num_pd_w_pdmp           0.0104664  0.0022420    4.668 3.25e-06 ***
## num_pd_w_medicaid       0.0223990  0.0042380    5.285 1.40e-07 ***
## Intervention_Redefined -0.0609092  0.0244971   -2.486 0.012989 *  
## lag_num_pd_w_tx        -0.0140202  0.0018155   -7.722 1.83e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df     F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   4.781  5.844 95.38  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 8.525  8.934 61.79  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     5.798  6.947 63.35  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      4.177  5.173 40.06  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.843   Deviance explained = 84.9%
## GCV = 0.087961  Scale est. = 0.084342  n = 2000
plot(sensitivity_anlys_lin_post_tx_model_log_smoothed_time, pages = 1)

7.5.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_smoothed_time <-
  data.frame(predict(sensitivity_anlys_lin_post_tx_model_log_smoothed_time, type = "lpmatrix"))

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_lin_post_tx_log_smoothed_time <- coef(sensitivity_anlys_lin_post_tx_model_log_smoothed_time)

sensitivity_anlys_lin_post_tx_sd_and_ci_log_smoothed_time <- 
  compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_smoothed_time), 
                    log(sensitivity_anlys_event_study_data$prop_dead),
                    coefficient_values_sensitivity_anlys_lin_post_tx_log_smoothed_time, 
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_smoothed_time) - 50)
round(sensitivity_anlys_lin_post_tx_sd_and_ci_log_smoothed_time, 3)
##                                                lb_coef coef_values ub_coef
## (Intercept)                                    -10.059      -9.818  -9.578
## StateAlaska                                      0.079       0.417   0.755
## StateArizona                                     0.128       0.376   0.624
## StateArkansas                                   -0.722      -0.406  -0.090
## StateCalifornia                                 -0.187       0.164   0.515
## StateColorado                                   -0.007       0.302   0.612
## StateConnecticut                                -0.016       0.345   0.707
## StateDelaware                                    0.036       0.316   0.596
## StateFlorida                                     0.286       0.566   0.846
## StateGeorgia                                     0.033       0.315   0.598
## StateHawaii                                     -0.676      -0.315   0.046
## StateIdaho                                      -0.621      -0.351  -0.080
## StateIllinois                                   -0.014       0.276   0.566
## StateIndiana                                    -0.453      -0.103   0.248
## StateIowa                                       -0.905      -0.600  -0.295
## StateKansas                                     -0.439      -0.164   0.111
## StateKentucky                                    0.216       0.516   0.816
## StateLouisiana                                   0.164       0.450   0.736
## StateMaine                                       0.008       0.383   0.757
## StateMaryland                                   -1.600      -1.258  -0.916
## StateMassachusetts                              -0.657      -0.158   0.341
## StateMichigan                                   -0.251       0.058   0.367
## StateMinnesota                                  -0.707      -0.403  -0.099
## StateMississippi                                -0.426      -0.142   0.142
## StateMissouri                                    0.180       0.457   0.735
## StateMontana                                    -0.287       0.000   0.287
## StateNebraska                                   -1.115      -0.818  -0.520
## StateNevada                                      0.332       0.655   0.977
## StateNew Hampshire                              -0.004       0.321   0.645
## StateNew Jersey                                  0.036       0.346   0.656
## StateNew Mexico                                  0.465       0.792   1.120
## StateNew York                                   -0.538      -0.199   0.140
## StateNorth Carolina                              0.054       0.314   0.575
## StateNorth Dakota                               -1.496      -1.176  -0.856
## StateOhio                                        0.339       0.668   0.997
## StateOklahoma                                    0.002       0.306   0.609
## StateOregon                                     -0.176       0.154   0.485
## StatePennsylvania                                0.286       0.621   0.956
## StateRhode Island                               -0.835      -0.283   0.270
## StateSouth Carolina                             -0.161       0.134   0.429
## StateSouth Dakota                               -1.370      -1.031  -0.691
## StateTennessee                                   0.146       0.424   0.701
## StateTexas                                      -0.287      -0.006   0.275
## StateUtah                                       -0.505      -0.180   0.144
## StateVermont                                    -0.246       0.068   0.383
## StateVirginia                                   -0.271      -0.007   0.257
## StateWashington                                  0.061       0.378   0.695
## StateWest Virginia                               0.251       0.586   0.922
## StateWisconsin                                  -0.111       0.180   0.471
## StateWyoming                                    -0.378      -0.106   0.167
## num_pd_w_naloxone_yes                           -0.067      -0.027   0.012
## num_pd_w_naloxone_no                            -0.028      -0.012   0.004
## num_pd_w_med_marijuana                          -0.020      -0.008   0.005
## num_pd_w_rec_marijuana                          -0.070      -0.023   0.024
## num_pd_w_gsl                                    -0.007       0.015   0.036
## num_pd_w_pdmp                                    0.000       0.010   0.021
## num_pd_w_medicaid                               -0.005       0.022   0.050
## Intervention_Redefined                          -0.161      -0.061   0.039
## lag_num_pd_w_tx                                 -0.023      -0.014  -0.005
## s(Time_Period_ID):as.factor(Region)Midwest.1    -0.659      -0.455  -0.251
## s(Time_Period_ID):as.factor(Region)Midwest.2    -0.365      -0.181   0.003
## s(Time_Period_ID):as.factor(Region)Midwest.3    -0.021       0.121   0.262
## s(Time_Period_ID):as.factor(Region)Midwest.4     0.191       0.323   0.456
## s(Time_Period_ID):as.factor(Region)Midwest.5     0.248       0.454   0.660
## s(Time_Period_ID):as.factor(Region)Midwest.6     0.452       0.621   0.790
## s(Time_Period_ID):as.factor(Region)Midwest.7     0.612       0.833   1.053
## s(Time_Period_ID):as.factor(Region)Midwest.8     0.677       1.095   1.512
## s(Time_Period_ID):as.factor(Region)Midwest.9     0.413       1.050   1.686
## s(Time_Period_ID):as.factor(Region)Northeast.1  -0.884      -0.521  -0.157
## s(Time_Period_ID):as.factor(Region)Northeast.2  -0.633      -0.352  -0.071
## s(Time_Period_ID):as.factor(Region)Northeast.3   0.077       0.319   0.562
## s(Time_Period_ID):as.factor(Region)Northeast.4   0.005       0.221   0.438
## s(Time_Period_ID):as.factor(Region)Northeast.5   0.048       0.363   0.678
## s(Time_Period_ID):as.factor(Region)Northeast.6   0.337       0.629   0.921
## s(Time_Period_ID):as.factor(Region)Northeast.7   0.669       0.997   1.324
## s(Time_Period_ID):as.factor(Region)Northeast.8   0.790       1.421   2.053
## s(Time_Period_ID):as.factor(Region)Northeast.9   0.193       1.196   2.199
## s(Time_Period_ID):as.factor(Region)South.1      -0.507      -0.328  -0.150
## s(Time_Period_ID):as.factor(Region)South.2      -0.235      -0.086   0.063
## s(Time_Period_ID):as.factor(Region)South.3       0.019       0.141   0.262
## s(Time_Period_ID):as.factor(Region)South.4       0.176       0.279   0.382
## s(Time_Period_ID):as.factor(Region)South.5       0.221       0.381   0.541
## s(Time_Period_ID):as.factor(Region)South.6       0.333       0.494   0.655
## s(Time_Period_ID):as.factor(Region)South.7       0.492       0.698   0.903
## s(Time_Period_ID):as.factor(Region)South.8       0.624       0.995   1.365
## s(Time_Period_ID):as.factor(Region)South.9       0.384       0.945   1.506
## s(Time_Period_ID):as.factor(Region)West.1       -0.441      -0.272  -0.103
## s(Time_Period_ID):as.factor(Region)West.2       -0.222      -0.075   0.072
## s(Time_Period_ID):as.factor(Region)West.3        0.013       0.130   0.248
## s(Time_Period_ID):as.factor(Region)West.4        0.181       0.291   0.401
## s(Time_Period_ID):as.factor(Region)West.5        0.208       0.391   0.575
## s(Time_Period_ID):as.factor(Region)West.6        0.273       0.459   0.644
## s(Time_Period_ID):as.factor(Region)West.7        0.294       0.515   0.735
## s(Time_Period_ID):as.factor(Region)West.8        0.318       0.657   0.995
## s(Time_Period_ID):as.factor(Region)West.9        0.139       0.656   1.173
##                                                sd_coef
## (Intercept)                                      0.123
## StateAlaska                                      0.172
## StateArizona                                     0.127
## StateArkansas                                    0.161
## StateCalifornia                                  0.179
## StateColorado                                    0.158
## StateConnecticut                                 0.184
## StateDelaware                                    0.143
## StateFlorida                                     0.143
## StateGeorgia                                     0.144
## StateHawaii                                      0.184
## StateIdaho                                       0.138
## StateIllinois                                    0.148
## StateIndiana                                     0.179
## StateIowa                                        0.156
## StateKansas                                      0.140
## StateKentucky                                    0.153
## StateLouisiana                                   0.146
## StateMaine                                       0.191
## StateMaryland                                    0.174
## StateMassachusetts                               0.255
## StateMichigan                                    0.157
## StateMinnesota                                   0.155
## StateMississippi                                 0.145
## StateMissouri                                    0.142
## StateMontana                                     0.146
## StateNebraska                                    0.152
## StateNevada                                      0.165
## StateNew Hampshire                               0.166
## StateNew Jersey                                  0.158
## StateNew Mexico                                  0.167
## StateNew York                                    0.173
## StateNorth Carolina                              0.133
## StateNorth Dakota                                0.163
## StateOhio                                        0.168
## StateOklahoma                                    0.155
## StateOregon                                      0.169
## StatePennsylvania                                0.171
## StateRhode Island                                0.282
## StateSouth Carolina                              0.150
## StateSouth Dakota                                0.173
## StateTennessee                                   0.142
## StateTexas                                       0.143
## StateUtah                                        0.166
## StateVermont                                     0.161
## StateVirginia                                    0.135
## StateWashington                                  0.162
## StateWest Virginia                               0.171
## StateWisconsin                                   0.148
## StateWyoming                                     0.139
## num_pd_w_naloxone_yes                            0.020
## num_pd_w_naloxone_no                             0.008
## num_pd_w_med_marijuana                           0.006
## num_pd_w_rec_marijuana                           0.024
## num_pd_w_gsl                                     0.011
## num_pd_w_pdmp                                    0.005
## num_pd_w_medicaid                                0.014
## Intervention_Redefined                           0.051
## lag_num_pd_w_tx                                  0.005
## s(Time_Period_ID):as.factor(Region)Midwest.1     0.104
## s(Time_Period_ID):as.factor(Region)Midwest.2     0.094
## s(Time_Period_ID):as.factor(Region)Midwest.3     0.072
## s(Time_Period_ID):as.factor(Region)Midwest.4     0.068
## s(Time_Period_ID):as.factor(Region)Midwest.5     0.105
## s(Time_Period_ID):as.factor(Region)Midwest.6     0.086
## s(Time_Period_ID):as.factor(Region)Midwest.7     0.113
## s(Time_Period_ID):as.factor(Region)Midwest.8     0.213
## s(Time_Period_ID):as.factor(Region)Midwest.9     0.325
## s(Time_Period_ID):as.factor(Region)Northeast.1   0.185
## s(Time_Period_ID):as.factor(Region)Northeast.2   0.143
## s(Time_Period_ID):as.factor(Region)Northeast.3   0.124
## s(Time_Period_ID):as.factor(Region)Northeast.4   0.110
## s(Time_Period_ID):as.factor(Region)Northeast.5   0.161
## s(Time_Period_ID):as.factor(Region)Northeast.6   0.149
## s(Time_Period_ID):as.factor(Region)Northeast.7   0.167
## s(Time_Period_ID):as.factor(Region)Northeast.8   0.322
## s(Time_Period_ID):as.factor(Region)Northeast.9   0.512
## s(Time_Period_ID):as.factor(Region)South.1       0.091
## s(Time_Period_ID):as.factor(Region)South.2       0.076
## s(Time_Period_ID):as.factor(Region)South.3       0.062
## s(Time_Period_ID):as.factor(Region)South.4       0.052
## s(Time_Period_ID):as.factor(Region)South.5       0.082
## s(Time_Period_ID):as.factor(Region)South.6       0.082
## s(Time_Period_ID):as.factor(Region)South.7       0.105
## s(Time_Period_ID):as.factor(Region)South.8       0.189
## s(Time_Period_ID):as.factor(Region)South.9       0.286
## s(Time_Period_ID):as.factor(Region)West.1        0.086
## s(Time_Period_ID):as.factor(Region)West.2        0.075
## s(Time_Period_ID):as.factor(Region)West.3        0.060
## s(Time_Period_ID):as.factor(Region)West.4        0.056
## s(Time_Period_ID):as.factor(Region)West.5        0.094
## s(Time_Period_ID):as.factor(Region)West.6        0.095
## s(Time_Period_ID):as.factor(Region)West.7        0.113
## s(Time_Period_ID):as.factor(Region)West.8        0.173
## s(Time_Period_ID):as.factor(Region)West.9        0.264

7.5.2 Attributable Deaths

date_data <- sensitivity_anlys_event_study_data_lin_post_tx[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_smoothed_time_lin_post <- attr_death_compute(sensitivity_anlys_event_study_data_lin_post_tx,
                                                                sensitivity_anlys_lin_post_tx_sd_and_ci_log_smoothed_time, 
                                                        post_tx_model = FALSE, tx_name = "num_pd_w_tx")
attr_deaths_est_log_smoothed_time_lin_post <- merge(attr_deaths_est_log_smoothed_time_lin_post, date_data, 
                                                    by.x = "Time_Period", by.y = "Time_Period_ID")

ggplot(attr_deaths_est_log_smoothed_time_lin_post, aes(x = Time_Period_Start)) + 
  # geom_point(aes(y = attr_deaths)) + 
  geom_line(aes(y = attr_deaths, linetype = "Estimate")) + 
  # geom_point(aes(y = attr_deaths_lb)) + 
  geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) + 
  # geom_point(aes(y = attr_deaths_ub)) + 
  geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) + 
  labs(x = "Date", y = "Attributable Deaths",
       title = "Estimated Number of Attributable Deaths Using Smoothed Time Effects, 
       Log Probability of Drug Overdose Death, Linear Policy Effects",
       linetype = "") + 
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black")) + 
  scale_linetype_manual(values = c("dashed", "solid"))

7.6 Analysis With Only Periods After Treatment Subset Periods

formula_post_tx_log_smoothed_time <- formula(paste("log(prop_dead)~ State +
                                           s(Time_Period_ID, bs = 'cr', by = as.factor(Region))  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(29 - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
data_subset <- sensitivity_anlys_event_study_data[sensitivity_anlys_event_study_data$Time_Period_ID <= 29,]
sensitivity_anlys_post_tx_model_log_smoothed_time_subset<-gam(formula_post_tx_log_smoothed_time,
                                         data = data_subset)
summary(sensitivity_anlys_post_tx_model_log_smoothed_time_subset)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## log(prop_dead) ~ State + s(Time_Period_ID, bs = "cr", by = as.factor(Region)) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + pos_4_pd + pos_5_pd + 
##     pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + pos_10_pd + pos_11_pd + 
##     pos_12_pd + pos_13_pd + pos_14_pd + pos_15_pd + pos_16_pd + 
##     pos_17_pd + pos_18_pd + pos_19_pd + pos_20_pd + pos_21_pd + 
##     pos_22_pd + pos_23_pd + pos_24_pd + pos_25_pd + pos_26_pd + 
##     pos_27_pd + pos_28_pd
## 
## Parametric coefficients:
##                                   Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -9.862725   0.059773 -165.004  < 2e-16 ***
## StateAlaska                       0.212414   0.090977    2.335 0.019699 *  
## StateArizona                      0.362667   0.079584    4.557 5.66e-06 ***
## StateArkansas                    -0.530538   0.079466   -6.676 3.57e-11 ***
## StateCalifornia                   0.193632   0.095742    2.022 0.043328 *  
## StateColorado                     0.090068   0.089227    1.009 0.312949    
## StateConnecticut                  0.314760   0.088485    3.557 0.000388 ***
## StateDelaware                     0.083216   0.080454    1.034 0.301169    
## StateFlorida                      0.537193   0.083477    6.435 1.71e-10 ***
## StateGeorgia                      0.224657   0.085947    2.614 0.009051 ** 
## StateHawaii                      -0.347263   0.089344   -3.887 0.000107 ***
## StateIdaho                       -0.110161   0.079916   -1.378 0.168290    
## StateIllinois                     0.458008   0.084604    5.414 7.30e-08 ***
## StateIndiana                     -0.004068   0.078860   -0.052 0.958866    
## StateIowa                        -0.611468   0.078991   -7.741 1.92e-14 ***
## StateKansas                      -0.170941   0.078231   -2.185 0.029054 *  
## StateKentucky                     0.727742   0.079503    9.154  < 2e-16 ***
## StateLouisiana                    0.446253   0.079310    5.627 2.23e-08 ***
## StateMaine                        0.010420   0.088712    0.117 0.906514    
## StateMaryland                    -1.670260   0.083298  -20.052  < 2e-16 ***
## StateMassachusetts               -0.239084   0.079192   -3.019 0.002584 ** 
## StateMichigan                     0.082081   0.080795    1.016 0.309849    
## StateMinnesota                   -0.602405   0.084229   -7.152 1.40e-12 ***
## StateMississippi                 -0.005186   0.079223   -0.065 0.947818    
## StateMissouri                     0.205192   0.080431    2.551 0.010846 *  
## StateMontana                     -0.245674   0.085185   -2.884 0.003989 ** 
## StateNebraska                    -0.924887   0.079776  -11.594  < 2e-16 ***
## StateNevada                       0.702655   0.087215    8.057 1.71e-15 ***
## StateNew Hampshire               -0.004402   0.079592   -0.055 0.955904    
## StateNew Jersey                   0.178997   0.081931    2.185 0.029080 *  
## StateNew Mexico                   0.891722   0.095342    9.353  < 2e-16 ***
## StateNew York                    -0.024124   0.084196   -0.287 0.774524    
## StateNorth Carolina               0.320215   0.078953    4.056 5.28e-05 ***
## StateNorth Dakota                -1.280818   0.078923  -16.229  < 2e-16 ***
## StateOhio                         0.577535   0.085178    6.780 1.79e-11 ***
## StateOklahoma                     0.571781   0.079148    7.224 8.40e-13 ***
## StateOregon                      -0.179475   0.089597   -2.003 0.045362 *  
## StatePennsylvania                 0.759541   0.083695    9.075  < 2e-16 ***
## StateRhode Island                -0.520918   0.083581   -6.232 6.13e-10 ***
## StateSouth Carolina               0.159320   0.079254    2.010 0.044604 *  
## StateSouth Dakota                -1.147427   0.079829  -14.374  < 2e-16 ***
## StateTennessee                    0.466473   0.078090    5.974 2.97e-09 ***
## StateTexas                        0.282478   0.082866    3.409 0.000672 ***
## StateUtah                        -0.095084   0.079262   -1.200 0.230497    
## StateVermont                     -0.175811   0.083479   -2.106 0.035383 *  
## StateVirginia                     0.065475   0.080026    0.818 0.413407    
## StateWashington                   0.212332   0.090920    2.335 0.019670 *  
## StateWest Virginia                0.732124   0.079582    9.200  < 2e-16 ***
## StateWisconsin                    0.037389   0.079858    0.468 0.639723    
## StateWyoming                      0.019764   0.078216    0.253 0.800547    
## Naloxone_Pharmacy_Yes_Redefined  -0.284390   0.082934   -3.429 0.000624 ***
## Naloxone_Pharmacy_No_Redefined   -0.086503   0.057196   -1.512 0.130668    
## Medical_Marijuana_Redefined       0.184293   0.042111    4.376 1.30e-05 ***
## Recreational_Marijuana_Redefined -0.109736   0.145171   -0.756 0.449838    
## GSL_Redefined                     0.045889   0.051826    0.885 0.376081    
## PDMP_Redefined                   -0.200586   0.028819   -6.960 5.28e-12 ***
## Medicaid_Expansion_Redefined     -0.017545   0.054275   -0.323 0.746552    
## pos_0_pd                         -0.013641   0.049650   -0.275 0.783552    
## pos_1_pd                         -0.071942   0.050652   -1.420 0.155746    
## pos_2_pd                         -0.025125   0.051288   -0.490 0.624297    
## pos_3_pd                         -0.071828   0.053549   -1.341 0.180032    
## pos_4_pd                         -0.071123   0.054886   -1.296 0.195252    
## pos_5_pd                         -0.106578   0.055901   -1.907 0.056792 .  
## pos_6_pd                         -0.134623   0.057990   -2.321 0.020409 *  
## pos_7_pd                         -0.126421   0.059190   -2.136 0.032870 *  
## pos_8_pd                         -0.166563   0.060121   -2.770 0.005674 ** 
## pos_9_pd                         -0.208846   0.063200   -3.305 0.000976 ***
## pos_10_pd                        -0.244293   0.066207   -3.690 0.000233 ***
## pos_11_pd                        -0.229367   0.067742   -3.386 0.000730 ***
## pos_12_pd                        -0.257327   0.069765   -3.689 0.000235 ***
## pos_13_pd                        -0.365723   0.074808   -4.889 1.14e-06 ***
## pos_14_pd                        -0.350234   0.079677   -4.396 1.19e-05 ***
## pos_15_pd                        -0.264112   0.080681   -3.274 0.001089 ** 
## pos_16_pd                        -0.296031   0.081807   -3.619 0.000307 ***
## pos_17_pd                        -0.311984   0.083093   -3.755 0.000181 ***
## pos_18_pd                        -0.307130   0.091697   -3.349 0.000832 ***
## pos_19_pd                        -0.281092   0.095203   -2.953 0.003206 ** 
## pos_20_pd                        -0.285711   0.098787   -2.892 0.003887 ** 
## pos_21_pd                        -0.328115   0.110391   -2.972 0.003008 ** 
## pos_22_pd                        -0.345412   0.116534   -2.964 0.003090 ** 
## pos_23_pd                        -0.393804   0.118868   -3.313 0.000948 ***
## pos_24_pd                        -0.529046   0.137904   -3.836 0.000131 ***
## pos_25_pd                        -0.546115   0.139495   -3.915 9.49e-05 ***
## pos_26_pd                        -0.522451   0.166403   -3.140 0.001728 ** 
## pos_27_pd                        -0.437444   0.225048   -1.944 0.052130 .  
## pos_28_pd                        -0.244808   0.228925   -1.069 0.285088    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                                edf Ref.df      F p-value    
## s(Time_Period_ID):as.factor(Region)Midwest   2.429  3.029 206.58  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)Northeast 7.447  8.397  64.25  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)South     2.857  3.558 179.50  <2e-16 ***
## s(Time_Period_ID):as.factor(Region)West      2.302  2.878 127.07  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.816   Deviance explained = 82.9%
## GCV = 0.094699  Scale est. = 0.0881    n = 1450

7.6.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time_subset <-
  data.frame(predict(sensitivity_anlys_post_tx_model_log_smoothed_time_subset, type = "lpmatrix"))

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time_subset <- coef(sensitivity_anlys_post_tx_model_log_smoothed_time_subset)

sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset <- 
  compute_sd_and_CI(as.matrix(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time_subset), 
                    log(data_subset$prop_dead),
                    coefficient_values_sensitivity_anlys_post_tx_log_smoothed_time_subset,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_smoothed_time_subset) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset
##                                                     lb_coef  coef_values
## (Intercept)                                    -9.973242764 -9.862725482
## StateAlaska                                     0.030029695  0.212414446
## StateArizona                                    0.235473910  0.362667104
## StateArkansas                                  -0.669357583 -0.530537691
## StateCalifornia                                 0.017783771  0.193631956
## StateColorado                                  -0.065292619  0.090068337
## StateConnecticut                                0.135999538  0.314759770
## StateDelaware                                  -0.063735645  0.083215545
## StateFlorida                                    0.410868395  0.537193243
## StateGeorgia                                    0.100095122  0.224657142
## StateHawaii                                    -0.507826084 -0.347262824
## StateIdaho                                     -0.234424109 -0.110161183
## StateIllinois                                   0.325912939  0.458007875
## StateIndiana                                   -0.120693237 -0.004068115
## StateIowa                                      -0.741281924 -0.611468419
## StateKansas                                    -0.288051105 -0.170941069
## StateKentucky                                   0.616746282  0.727741657
## StateLouisiana                                  0.321049907  0.446253201
## StateMaine                                     -0.177528437  0.010419932
## StateMaryland                                  -1.868203240 -1.670260245
## StateMassachusetts                             -0.508779128 -0.239083840
## StateMichigan                                  -0.031501236  0.082080926
## StateMinnesota                                 -0.740527224 -0.602404704
## StateMississippi                               -0.123799504 -0.005185847
## StateMissouri                                   0.096518983  0.205191613
## StateMontana                                   -0.385556467 -0.245673894
## StateNebraska                                  -1.043938298 -0.924886581
## StateNevada                                     0.566172640  0.702654874
## StateNew Hampshire                             -0.148090598 -0.004401802
## StateNew Jersey                                -0.011379492  0.178997370
## StateNew Mexico                                 0.706962026  0.891721593
## StateNew York                                  -0.176639545 -0.024123712
## StateNorth Carolina                             0.217134430  0.320214716
## StateNorth Dakota                              -1.491629505 -1.280818174
## StateOhio                                       0.425900211  0.577535139
## StateOklahoma                                   0.460835760  0.571781079
## StateOregon                                    -0.334250654 -0.179475237
## StatePennsylvania                               0.625509542  0.759541236
## StateRhode Island                              -0.908033445 -0.520917738
## StateSouth Carolina                             0.038306724  0.159320137
## StateSouth Dakota                              -1.307649853 -1.147426537
## StateTennessee                                  0.360071601  0.466472779
## StateTexas                                      0.154841933  0.282477733
## StateUtah                                      -0.297147646 -0.095083851
## StateVermont                                   -0.357220539 -0.175811301
## StateVirginia                                  -0.054840847  0.065474678
## StateWashington                                 0.057295704  0.212331764
## StateWest Virginia                              0.551757191  0.732123709
## StateWisconsin                                 -0.071393881  0.037388815
## StateWyoming                                   -0.132491707  0.019764436
## Naloxone_Pharmacy_Yes_Redefined                -0.402616193 -0.284390220
## Naloxone_Pharmacy_No_Redefined                 -0.205794848 -0.086502721
## Medical_Marijuana_Redefined                     0.079208577  0.184292505
## Recreational_Marijuana_Redefined               -0.278228478 -0.109735670
## GSL_Redefined                                  -0.054615051  0.045888641
## PDMP_Redefined                                 -0.257222183 -0.200585732
## Medicaid_Expansion_Redefined                   -0.107491848 -0.017544585
## pos_0_pd                                       -0.099925615 -0.013641245
## pos_1_pd                                       -0.167291650 -0.071941536
## pos_2_pd                                       -0.105556368 -0.025124924
## pos_3_pd                                       -0.154038586 -0.071827871
## pos_4_pd                                       -0.150512944 -0.071123103
## pos_5_pd                                       -0.193500070 -0.106577884
## pos_6_pd                                       -0.231858556 -0.134622844
## pos_7_pd                                       -0.231502747 -0.126420780
## pos_8_pd                                       -0.262459251 -0.166562838
## pos_9_pd                                       -0.320178960 -0.208846260
## pos_10_pd                                      -0.369801838 -0.244293238
## pos_11_pd                                      -0.338478739 -0.229366928
## pos_12_pd                                      -0.379824201 -0.257327000
## pos_13_pd                                      -0.531192866 -0.365723111
## pos_14_pd                                      -0.524590515 -0.350234166
## pos_15_pd                                      -0.391752279 -0.264111549
## pos_16_pd                                      -0.437541338 -0.296030852
## pos_17_pd                                      -0.458735161 -0.311983614
## pos_18_pd                                      -0.471358331 -0.307129986
## pos_19_pd                                      -0.438420814 -0.281091994
## pos_20_pd                                      -0.463836535 -0.285710584
## pos_21_pd                                      -0.562884149 -0.328114602
## pos_22_pd                                      -0.613816528 -0.345411706
## pos_23_pd                                      -0.648454982 -0.393804343
## pos_24_pd                                      -0.745318376 -0.529045906
## pos_25_pd                                      -0.767274756 -0.546115201
## pos_26_pd                                      -0.798404490 -0.522450793
## pos_27_pd                                      -0.664142924 -0.437444010
## pos_28_pd                                      -0.461949852 -0.244808392
## s(Time_Period_ID):as.factor(Region)Midwest.1   -0.534848240 -0.435880992
## s(Time_Period_ID):as.factor(Region)Midwest.2   -0.326382928 -0.237608613
## s(Time_Period_ID):as.factor(Region)Midwest.3   -0.090492660  0.010782212
## s(Time_Period_ID):as.factor(Region)Midwest.4    0.137266609  0.233869614
## s(Time_Period_ID):as.factor(Region)Midwest.5    0.333757553  0.439242815
## s(Time_Period_ID):as.factor(Region)Midwest.6    0.531352147  0.621167429
## s(Time_Period_ID):as.factor(Region)Midwest.7    0.663382014  0.770061218
## s(Time_Period_ID):as.factor(Region)Midwest.8    0.849363529  0.963521101
## s(Time_Period_ID):as.factor(Region)Midwest.9    0.843682581  0.960091243
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.741889256 -0.459073113
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.527521719 -0.291441706
## s(Time_Period_ID):as.factor(Region)Northeast.3 -0.311926440 -0.054312038
## s(Time_Period_ID):as.factor(Region)Northeast.4  0.310402416  0.499558659
## s(Time_Period_ID):as.factor(Region)Northeast.5  0.390052304  0.585604773
## s(Time_Period_ID):as.factor(Region)Northeast.6  0.290344230  0.504138247
## s(Time_Period_ID):as.factor(Region)Northeast.7  0.443993825  0.639736699
## s(Time_Period_ID):as.factor(Region)Northeast.8  0.716344533  0.917205803
## s(Time_Period_ID):as.factor(Region)Northeast.9  0.870381499  1.091103894
## s(Time_Period_ID):as.factor(Region)South.1     -0.467345778 -0.381056024
## s(Time_Period_ID):as.factor(Region)South.2     -0.241859170 -0.167637612
## s(Time_Period_ID):as.factor(Region)South.3     -0.007180722  0.069613509
## s(Time_Period_ID):as.factor(Region)South.4      0.187031499  0.265394961
## s(Time_Period_ID):as.factor(Region)South.5      0.354470163  0.430160759
## s(Time_Period_ID):as.factor(Region)South.6      0.484595451  0.569532471
## s(Time_Period_ID):as.factor(Region)South.7      0.600966960  0.685448745
## s(Time_Period_ID):as.factor(Region)South.8      0.749582832  0.851122838
## s(Time_Period_ID):as.factor(Region)South.9      0.705110292  0.834017294
## s(Time_Period_ID):as.factor(Region)West.1      -0.422746695 -0.304616044
## s(Time_Period_ID):as.factor(Region)West.2      -0.242255731 -0.156595834
## s(Time_Period_ID):as.factor(Region)West.3      -0.070184131  0.015901091
## s(Time_Period_ID):as.factor(Region)West.4       0.089618625  0.168392108
## s(Time_Period_ID):as.factor(Region)West.5       0.236401125  0.313119188
## s(Time_Period_ID):as.factor(Region)West.6       0.363290257  0.443694096
## s(Time_Period_ID):as.factor(Region)West.7       0.460635234  0.550484292
## s(Time_Period_ID):as.factor(Region)West.8       0.574372960  0.689663400
## s(Time_Period_ID):as.factor(Region)West.9       0.514004682  0.687288177
##                                                     ub_coef    sd_coef
## (Intercept)                                    -9.752208201 0.05638637
## StateAlaska                                     0.394799197 0.09305344
## StateArizona                                    0.489860298 0.06489449
## StateArkansas                                  -0.391717800 0.07082648
## StateCalifornia                                 0.369480141 0.08971846
## StateColorado                                   0.245429293 0.07926579
## StateConnecticut                                0.493520002 0.09120420
## StateDelaware                                   0.230166734 0.07497510
## StateFlorida                                    0.663518090 0.06445145
## StateGeorgia                                    0.349219162 0.06355205
## StateHawaii                                    -0.186699564 0.08192003
## StateIdaho                                      0.014101743 0.06339945
## StateIllinois                                   0.590102812 0.06739538
## StateIndiana                                    0.112557007 0.05950261
## StateIowa                                      -0.481654913 0.06623138
## StateKansas                                    -0.053831034 0.05975002
## StateKentucky                                   0.838737032 0.05663029
## StateLouisiana                                  0.571456495 0.06387923
## StateMaine                                      0.198368301 0.09589202
## StateMaryland                                  -1.472317250 0.10099132
## StateMassachusetts                              0.030611449 0.13759964
## StateMichigan                                   0.195663087 0.05795008
## StateMinnesota                                 -0.464282184 0.07047067
## StateMississippi                                0.113427809 0.06051717
## StateMissouri                                   0.313864243 0.05544522
## StateMontana                                   -0.105791320 0.07136866
## StateNebraska                                  -0.805834864 0.06074067
## StateNevada                                     0.839137108 0.06963379
## StateNew Hampshire                              0.139286993 0.07331061
## StateNew Jersey                                 0.369374232 0.09713105
## StateNew Mexico                                 1.076481160 0.09426509
## StateNew York                                   0.128392122 0.07781420
## StateNorth Carolina                             0.423295003 0.05259198
## StateNorth Dakota                              -1.070006842 0.10755680
## StateOhio                                       0.729170068 0.07736476
## StateOklahoma                                   0.682726397 0.05660475
## StateOregon                                    -0.024699820 0.07896705
## StatePennsylvania                               0.893572930 0.06838352
## StateRhode Island                              -0.133802031 0.19750801
## StateSouth Carolina                             0.280333550 0.06174154
## StateSouth Dakota                              -0.987203221 0.08174659
## StateTennessee                                  0.572873956 0.05428632
## StateTexas                                      0.410113533 0.06512031
## StateUtah                                       0.106979945 0.10309377
## StateVermont                                    0.005597938 0.09255573
## StateVirginia                                   0.185790202 0.06138547
## StateWashington                                 0.367367825 0.07910003
## StateWest Virginia                              0.912490227 0.09202373
## StateWisconsin                                  0.146171511 0.05550138
## StateWyoming                                    0.172020579 0.07768171
## Naloxone_Pharmacy_Yes_Redefined                -0.166164247 0.06031937
## Naloxone_Pharmacy_No_Redefined                  0.032789407 0.06086333
## Medical_Marijuana_Redefined                     0.289376432 0.05361425
## Recreational_Marijuana_Redefined                0.058757138 0.08596572
## GSL_Redefined                                   0.146392333 0.05127739
## PDMP_Redefined                                 -0.143949281 0.02889615
## Medicaid_Expansion_Redefined                    0.072402679 0.04589146
## pos_0_pd                                        0.072643126 0.04402264
## pos_1_pd                                        0.023408579 0.04864802
## pos_2_pd                                        0.055306520 0.04103645
## pos_3_pd                                        0.010382844 0.04194424
## pos_4_pd                                        0.008266737 0.04050502
## pos_5_pd                                       -0.019655698 0.04434805
## pos_6_pd                                       -0.037387133 0.04961006
## pos_7_pd                                       -0.021338814 0.05361325
## pos_8_pd                                       -0.070666424 0.04892674
## pos_9_pd                                       -0.097513561 0.05680240
## pos_10_pd                                      -0.118784638 0.06403500
## pos_11_pd                                      -0.120255117 0.05566929
## pos_12_pd                                      -0.134829799 0.06249857
## pos_13_pd                                      -0.200253355 0.08442334
## pos_14_pd                                      -0.175877817 0.08895732
## pos_15_pd                                      -0.136470819 0.06512282
## pos_16_pd                                      -0.154520366 0.07219923
## pos_17_pd                                      -0.165232067 0.07487324
## pos_18_pd                                      -0.142901642 0.08378997
## pos_19_pd                                      -0.123763173 0.08026981
## pos_20_pd                                      -0.107584633 0.09088059
## pos_21_pd                                      -0.093345054 0.11978038
## pos_22_pd                                      -0.077006884 0.13694124
## pos_23_pd                                      -0.139153705 0.12992380
## pos_24_pd                                      -0.312773436 0.11034310
## pos_25_pd                                      -0.324955646 0.11283651
## pos_26_pd                                      -0.246497096 0.14079270
## pos_27_pd                                      -0.210745096 0.11566271
## pos_28_pd                                      -0.027666932 0.11078646
## s(Time_Period_ID):as.factor(Region)Midwest.1   -0.336913744 0.05049349
## s(Time_Period_ID):as.factor(Region)Midwest.2   -0.148834299 0.04529302
## s(Time_Period_ID):as.factor(Region)Midwest.3    0.112057084 0.05167085
## s(Time_Period_ID):as.factor(Region)Midwest.4    0.330472619 0.04928725
## s(Time_Period_ID):as.factor(Region)Midwest.5    0.544728077 0.05381901
## s(Time_Period_ID):as.factor(Region)Midwest.6    0.710982710 0.04582412
## s(Time_Period_ID):as.factor(Region)Midwest.7    0.876740422 0.05442817
## s(Time_Period_ID):as.factor(Region)Midwest.8    1.077678673 0.05824366
## s(Time_Period_ID):as.factor(Region)Midwest.9    1.076499906 0.05939217
## s(Time_Period_ID):as.factor(Region)Northeast.1 -0.176256970 0.14429395
## s(Time_Period_ID):as.factor(Region)Northeast.2 -0.055361694 0.12044899
## s(Time_Period_ID):as.factor(Region)Northeast.3  0.203302365 0.13143592
## s(Time_Period_ID):as.factor(Region)Northeast.4  0.688714902 0.09650829
## s(Time_Period_ID):as.factor(Region)Northeast.5  0.781157241 0.09977167
## s(Time_Period_ID):as.factor(Region)Northeast.6  0.717932264 0.10907858
## s(Time_Period_ID):as.factor(Region)Northeast.7  0.835479573 0.09986881
## s(Time_Period_ID):as.factor(Region)Northeast.8  1.118067073 0.10248024
## s(Time_Period_ID):as.factor(Region)Northeast.9  1.311826289 0.11261347
## s(Time_Period_ID):as.factor(Region)South.1     -0.294766271 0.04402538
## s(Time_Period_ID):as.factor(Region)South.2     -0.093416054 0.03786814
## s(Time_Period_ID):as.factor(Region)South.3      0.146407740 0.03918073
## s(Time_Period_ID):as.factor(Region)South.4      0.343758422 0.03998136
## s(Time_Period_ID):as.factor(Region)South.5      0.505851355 0.03861765
## s(Time_Period_ID):as.factor(Region)South.6      0.654469492 0.04333521
## s(Time_Period_ID):as.factor(Region)South.7      0.769930529 0.04310295
## s(Time_Period_ID):as.factor(Region)South.8      0.952662844 0.05180613
## s(Time_Period_ID):as.factor(Region)South.9      0.962924296 0.06576888
## s(Time_Period_ID):as.factor(Region)West.1      -0.186485393 0.06027074
## s(Time_Period_ID):as.factor(Region)West.2      -0.070935938 0.04370403
## s(Time_Period_ID):as.factor(Region)West.3       0.101986312 0.04392103
## s(Time_Period_ID):as.factor(Region)West.4       0.247165591 0.04019055
## s(Time_Period_ID):as.factor(Region)West.5       0.389837252 0.03914187
## s(Time_Period_ID):as.factor(Region)West.6       0.524097935 0.04102237
## s(Time_Period_ID):as.factor(Region)West.7       0.640333349 0.04584136
## s(Time_Period_ID):as.factor(Region)West.8       0.804953841 0.05882165
## s(Time_Period_ID):as.factor(Region)West.9       0.860571672 0.08840995

7.6.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_smoothed_time_subset <- sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_smoothed_time_subset)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(data_subset$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_smoothed_time_subset) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_smoothed_time_subset$num_states <- sapply(plot_post_tx_log_smoothed_time_subset$term,
                                                    function(x){sum(sensitivity_anlys_event_study_data[,x])})

plot_post_tx_data <- merge(plot_post_tx_log_smoothed_time, plot_post_tx_log_smoothed_time_subset, 
                           by = "term", all.x = TRUE)
plot_post_tx_data$term <- factor(plot_post_tx_data$term, 
                                                     levels = sapply(0:39, function(x){paste("pos_", x, "_pd", sep = "")}))
ggplot(plot_post_tx_data, aes(x = term)) +  
  geom_point(plot_post_tx_data, mapping = aes(y = estimate.y, color = "subset data")) + 
  geom_pointrange(plot_post_tx_data, 
                  mapping = aes(x = term, y = estimate.y, ymin = conf.low.y, ymax = conf.high.y, color = "subset data"),
                  fatten = 1, alpha = .5) + 
  geom_point(plot_post_tx_data, mapping = aes(y = estimate.x, color = "full data")) + 
  geom_pointrange(plot_post_tx_data, 
                  mapping = aes(x = term, y = estimate.x, ymin = conf.low.x, ymax = conf.high.x, color = "full data"),
                  fatten = 1, alpha = .5) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4),
        legend.position = "bottom") +
  geom_hline(aes(yintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods",
       color = "Full Data or Subset Times") 

  # geom_vline(aes(xintercept = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
  # geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"]), y = 12, 
  #           x = coef(main_analysis_model_log_smoothed_time)["Intervention_Redefined"] + 0.1), color = "red")
  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2) 

8 OLS Model Main Analysis With Fixed Time Effects Interacted with Region With Log Proportion

#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population


#fit an OLS with smoothed time effects
main_analysis_model_log_fixed_time<-lm(log(prop_dead)~ State +
                                         factor(Time_Period_ID) + 
                                         Naloxone_Pharmacy_Yes_Redefined +
                                         Naloxone_Pharmacy_No_Redefined +
                                         Medical_Marijuana_Redefined +
                                         Recreational_Marijuana_Redefined +
                                         GSL_Redefined +
                                         PDMP_Redefined +
                                         Medicaid_Expansion_Redefined +
                                         Intervention_Redefined ,
                                       data = main_analysis_data)

summary(main_analysis_model_log_fixed_time)
## 
## Call:
## lm(formula = log(prop_dead) ~ State + factor(Time_Period_ID) + 
##     Naloxone_Pharmacy_Yes_Redefined + Naloxone_Pharmacy_No_Redefined + 
##     Medical_Marijuana_Redefined + Recreational_Marijuana_Redefined + 
##     GSL_Redefined + PDMP_Redefined + Medicaid_Expansion_Redefined + 
##     Intervention_Redefined, data = main_analysis_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.16662 -0.14440  0.01557  0.16375  1.01553 
## 
## Coefficients:
##                                    Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -1.070e+01  6.658e-02 -160.743  < 2e-16 ***
## StateAlaska                       1.164e-01  7.781e-02    1.495  0.13498    
## StateArizona                      2.490e-01  7.153e-02    3.481  0.00051 ***
## StateArkansas                    -5.008e-01  7.062e-02   -7.092 1.86e-12 ***
## StateCalifornia                  -2.310e-01  7.771e-02   -2.973  0.00299 ** 
## StateColorado                     2.546e-03  7.741e-02    0.033  0.97377    
## StateConnecticut                  1.765e-01  7.464e-02    2.365  0.01812 *  
## StateDelaware                     1.793e-01  7.180e-02    2.497  0.01262 *  
## StateFlorida                      2.975e-01  7.066e-02    4.210 2.67e-05 ***
## StateGeorgia                      9.257e-04  7.067e-02    0.013  0.98955    
## StateHawaii                      -4.627e-01  7.666e-02   -6.036 1.90e-09 ***
## StateIdaho                       -1.269e-01  7.068e-02   -1.795  0.07284 .  
## StateIllinois                     1.306e-01  7.168e-02    1.822  0.06859 .  
## StateIndiana                      8.123e-02  7.029e-02    1.156  0.24798    
## StateIowa                        -6.772e-01  7.046e-02   -9.611  < 2e-16 ***
## StateKansas                      -2.301e-01  6.994e-02   -3.290  0.00102 ** 
## StateKentucky                     6.993e-01  7.077e-02    9.882  < 2e-16 ***
## StateLouisiana                    3.399e-01  6.985e-02    4.867 1.23e-06 ***
## StateMaine                        1.993e-02  7.758e-02    0.257  0.79726    
## StateMaryland                    -1.540e+00  7.152e-02  -21.525  < 2e-16 ***
## StateMassachusetts               -9.582e-02  7.113e-02   -1.347  0.17814    
## StateMichigan                    -3.275e-02  7.216e-02   -0.454  0.64994    
## StateMinnesota                   -7.108e-01  7.336e-02   -9.689  < 2e-16 ***
## StateMississippi                 -4.987e-02  6.990e-02   -0.713  0.47565    
## StateMissouri                     1.644e-01  7.223e-02    2.276  0.02294 *  
## StateMontana                     -5.026e-01  7.387e-02   -6.803 1.37e-11 ***
## StateNebraska                    -8.789e-01  7.103e-02  -12.373  < 2e-16 ***
## StateNevada                       4.032e-01  7.528e-02    5.357 9.50e-08 ***
## StateNew Hampshire                1.198e-01  7.095e-02    1.689  0.09144 .  
## StateNew Jersey                   4.021e-02  7.161e-02    0.562  0.57445    
## StateNew Mexico                   5.692e-01  7.626e-02    7.464 1.27e-13 ***
## StateNew York                    -1.778e-01  7.217e-02   -2.464  0.01384 *  
## StateNorth Carolina               2.328e-01  6.973e-02    3.338  0.00086 ***
## StateNorth Dakota                -1.151e+00  7.034e-02  -16.366  < 2e-16 ***
## StateOhio                         4.362e-01  7.083e-02    6.158 8.97e-10 ***
## StateOklahoma                     4.533e-01  7.036e-02    6.443 1.48e-10 ***
## StateOregon                      -3.275e-01  7.715e-02   -4.246 2.28e-05 ***
## StatePennsylvania                 5.452e-01  7.074e-02    7.707 2.05e-14 ***
## StateRhode Island                -3.432e-01  7.307e-02   -4.697 2.83e-06 ***
## StateSouth Carolina               2.059e-01  7.028e-02    2.930  0.00343 ** 
## StateSouth Dakota                -1.028e+00  7.069e-02  -14.538  < 2e-16 ***
## StateTennessee                    4.674e-01  6.955e-02    6.721 2.38e-11 ***
## StateTexas                       -2.100e-02  7.064e-02   -0.297  0.76627    
## StateUtah                        -1.021e-01  6.996e-02   -1.460  0.14450    
## StateVermont                     -2.267e-01  7.319e-02   -3.098  0.00198 ** 
## StateVirginia                    -3.502e-02  6.986e-02   -0.501  0.61623    
## StateWashington                   2.417e-03  7.834e-02    0.031  0.97539    
## StateWest Virginia                7.778e-01  7.074e-02   10.995  < 2e-16 ***
## StateWisconsin                    5.883e-03  7.000e-02    0.084  0.93303    
## StateWyoming                     -2.170e-02  6.991e-02   -0.310  0.75634    
## factor(Time_Period_ID)2          -4.194e-03  6.211e-02   -0.068  0.94618    
## factor(Time_Period_ID)3           1.132e-01  6.213e-02    1.822  0.06861 .  
## factor(Time_Period_ID)4           1.623e-01  6.217e-02    2.610  0.00911 ** 
## factor(Time_Period_ID)5           3.199e-01  6.219e-02    5.143 2.98e-07 ***
## factor(Time_Period_ID)6           3.397e-01  6.226e-02    5.455 5.52e-08 ***
## factor(Time_Period_ID)7           4.779e-01  6.229e-02    7.673 2.66e-14 ***
## factor(Time_Period_ID)8           4.621e-01  6.233e-02    7.413 1.85e-13 ***
## factor(Time_Period_ID)9           5.468e-01  6.242e-02    8.760  < 2e-16 ***
## factor(Time_Period_ID)10          5.440e-01  6.258e-02    8.693  < 2e-16 ***
## factor(Time_Period_ID)11          6.607e-01  6.270e-02   10.537  < 2e-16 ***
## factor(Time_Period_ID)12          6.757e-01  6.302e-02   10.722  < 2e-16 ***
## factor(Time_Period_ID)13          8.393e-01  6.322e-02   13.277  < 2e-16 ***
## factor(Time_Period_ID)14          8.891e-01  6.348e-02   14.005  < 2e-16 ***
## factor(Time_Period_ID)15          9.345e-01  6.348e-02   14.721  < 2e-16 ***
## factor(Time_Period_ID)16          9.466e-01  6.376e-02   14.846  < 2e-16 ***
## factor(Time_Period_ID)17          1.029e+00  6.432e-02   16.005  < 2e-16 ***
## factor(Time_Period_ID)18          1.030e+00  6.461e-02   15.947  < 2e-16 ***
## factor(Time_Period_ID)19          1.016e+00  6.485e-02   15.669  < 2e-16 ***
## factor(Time_Period_ID)20          1.021e+00  6.525e-02   15.645  < 2e-16 ***
## factor(Time_Period_ID)21          1.057e+00  6.559e-02   16.113  < 2e-16 ***
## factor(Time_Period_ID)22          1.024e+00  6.607e-02   15.499  < 2e-16 ***
## factor(Time_Period_ID)23          1.169e+00  6.633e-02   17.629  < 2e-16 ***
## factor(Time_Period_ID)24          1.162e+00  6.708e-02   17.325  < 2e-16 ***
## factor(Time_Period_ID)25          1.157e+00  6.731e-02   17.185  < 2e-16 ***
## factor(Time_Period_ID)26          1.160e+00  6.769e-02   17.135  < 2e-16 ***
## factor(Time_Period_ID)27          1.255e+00  6.836e-02   18.360  < 2e-16 ***
## factor(Time_Period_ID)28          1.224e+00  6.905e-02   17.727  < 2e-16 ***
## factor(Time_Period_ID)29          1.275e+00  6.993e-02   18.237  < 2e-16 ***
## factor(Time_Period_ID)30          1.283e+00  7.118e-02   18.019  < 2e-16 ***
## factor(Time_Period_ID)31          1.385e+00  7.188e-02   19.262  < 2e-16 ***
## factor(Time_Period_ID)32          1.414e+00  7.509e-02   18.834  < 2e-16 ***
## factor(Time_Period_ID)33          1.554e+00  7.663e-02   20.286  < 2e-16 ***
## factor(Time_Period_ID)34          1.583e+00  7.971e-02   19.857  < 2e-16 ***
## factor(Time_Period_ID)35          1.635e+00  8.065e-02   20.279  < 2e-16 ***
## factor(Time_Period_ID)36          1.643e+00  8.215e-02   20.005  < 2e-16 ***
## factor(Time_Period_ID)37          1.621e+00  8.220e-02   19.724  < 2e-16 ***
## factor(Time_Period_ID)38          1.593e+00  8.257e-02   19.298  < 2e-16 ***
## factor(Time_Period_ID)39          1.624e+00  8.282e-02   19.611  < 2e-16 ***
## factor(Time_Period_ID)40          1.683e+00  8.292e-02   20.302  < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined  -5.662e-02  4.607e-02   -1.229  0.21924    
## Naloxone_Pharmacy_No_Redefined    3.659e-02  3.916e-02    0.934  0.35022    
## Medical_Marijuana_Redefined       2.778e-01  3.084e-02    9.006  < 2e-16 ***
## Recreational_Marijuana_Redefined -2.535e-01  4.663e-02   -5.437 6.12e-08 ***
## GSL_Redefined                     4.494e-02  3.270e-02    1.374  0.16950    
## PDMP_Redefined                   -1.514e-01  2.593e-02   -5.839 6.15e-09 ***
## Medicaid_Expansion_Redefined      9.274e-02  3.195e-02    2.903  0.00374 ** 
## Intervention_Redefined           -2.813e-02  2.536e-02   -1.109  0.26742    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3105 on 1903 degrees of freedom
## Multiple R-squared:  0.8292, Adjusted R-squared:  0.8206 
## F-statistic: 96.25 on 96 and 1903 DF,  p-value: < 2.2e-16
#examine fitted values
summary(fitted(main_analysis_model_log_fixed_time))
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -12.246 -10.224  -9.743  -9.796  -9.334  -8.061
hist(fitted(main_analysis_model_log_fixed_time))

par(mfrow = c(2,2))
plot(main_analysis_model_log_fixed_time)

8.1 Coefficients and 95% CI

#compute the full dataset including basis functions
full_df_w_basis_functions_log_fixed_time <- model.matrix(main_analysis_model_log_fixed_time)

#estimate the 95% CI and SD
coefficient_values_log_fixed_time <- coef(main_analysis_model_log_fixed_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_fixed_time <- compute_sd_and_CI(full_df_w_basis_functions_log_fixed_time, log(main_analysis_data$prop_dead),
                                             coefficient_values_log_fixed_time,
                                             p = ncol(full_df_w_basis_functions_log_fixed_time) - 50)
main_analysis_sd_and_ci_log_fixed_time
##                                        lb_coef   coef_values      ub_coef
## (Intercept)                      -10.850377438 -1.070190e+01 -10.55342460
## StateAlaska                       -0.024222451  1.163638e-01   0.25695010
## StateArizona                       0.123163944  2.490087e-01   0.37485344
## StateArkansas                     -0.615183054 -5.008129e-01  -0.38644280
## StateCalifornia                   -0.366193094 -2.310104e-01  -0.09582777
## StateColorado                     -0.120489769  2.545702e-03   0.12558117
## StateConnecticut                   0.053335063  1.765235e-01   0.29971188
## StateDelaware                      0.060279724  1.792553e-01   0.29823083
## StateFlorida                       0.193187574  2.975306e-01   0.40187353
## StateGeorgia                      -0.083673688  9.256537e-04   0.08552500
## StateHawaii                       -0.581782815 -4.626592e-01  -0.34353560
## StateIdaho                        -0.223147224 -1.268582e-01  -0.03056909
## StateIllinois                      0.016246056  1.306158e-01   0.24498551
## StateIndiana                      -0.032281040  8.122898e-02   0.19473900
## StateIowa                         -0.776424451 -6.771603e-01  -0.57789615
## StateKansas                       -0.323691489 -2.300818e-01  -0.13647210
## StateKentucky                      0.614299989  6.993124e-01   0.78432472
## StateLouisiana                     0.249464265  3.399497e-01   0.43043520
## StateMaine                        -0.123748761  1.993242e-02   0.16361360
## StateMaryland                     -1.738187896 -1.539511e+00  -1.34083426
## StateMassachusetts                -0.343594890 -9.581610e-02   0.15196269
## StateMichigan                     -0.125622954 -3.275458e-02   0.06011379
## StateMinnesota                    -0.815653006 -7.107882e-01  -0.60592338
## StateMississippi                  -0.141559018 -4.987073e-02   0.04181756
## StateMissouri                      0.073234663  1.644191e-01   0.25560348
## StateMontana                      -0.636430671 -5.025719e-01  -0.36871321
## StateNebraska                     -0.979013715 -8.788536e-01  -0.77869348
## StateNevada                        0.263925040  4.032381e-01   0.54255124
## StateNew Hampshire                 0.007532138  1.198117e-01   0.23209117
## StateNew Jersey                   -0.112177572  4.021439e-02   0.19260636
## StateNew Mexico                    0.397124639  5.691988e-01   0.74127297
## StateNew York                     -0.277609783 -1.778175e-01  -0.07802516
## StateNorth Carolina                0.155235658  2.327622e-01   0.31028869
## StateNorth Dakota                 -1.304472017 -1.151218e+00  -0.99796355
## StateOhio                          0.334026326  4.361814e-01   0.53833657
## StateOklahoma                      0.339894506  4.533470e-01   0.56679950
## StateOregon                       -0.451327786 -3.275490e-01  -0.20377028
## StatePennsylvania                  0.459766169  5.452425e-01   0.63071874
## StateRhode Island                 -0.673140069 -3.431727e-01  -0.01320542
## StateSouth Carolina                0.120718786  2.059469e-01   0.29117500
## StateSouth Dakota                 -1.154314365 -1.027659e+00  -0.90100282
## StateTennessee                     0.387278412  4.674282e-01   0.54757791
## StateTexas                        -0.130893480 -2.100228e-02   0.08888893
## StateUtah                         -0.236806398 -1.021254e-01   0.03255555
## StateVermont                      -0.357143094 -2.267290e-01  -0.09631498
## StateVirginia                     -0.126891940 -3.502118e-02   0.05684958
## StateWashington                   -0.132368537  2.416598e-03   0.13720173
## StateWest Virginia                 0.638723984  7.777861e-01   0.91684822
## StateWisconsin                    -0.077941341  5.882776e-03   0.08970689
## StateWyoming                      -0.139555529 -2.169648e-02   0.09616258
## factor(Time_Period_ID)2           -0.182683926 -4.193465e-03   0.17429700
## factor(Time_Period_ID)3           -0.054097599  1.132110e-01   0.28051968
## factor(Time_Period_ID)4           -0.007798426  1.622897e-01   0.33237780
## factor(Time_Period_ID)5            0.136392992  3.198863e-01   0.50337959
## factor(Time_Period_ID)6            0.158159228  3.396625e-01   0.52116568
## factor(Time_Period_ID)7            0.311954493  4.779435e-01   0.64393259
## factor(Time_Period_ID)8            0.289110842  4.620562e-01   0.63500165
## factor(Time_Period_ID)9            0.365445134  5.468409e-01   0.72823668
## factor(Time_Period_ID)10           0.365866689  5.439792e-01   0.72209165
## factor(Time_Period_ID)11           0.505418833  6.607149e-01   0.81601088
## factor(Time_Period_ID)12           0.512055077  6.756633e-01   0.83927155
## factor(Time_Period_ID)13           0.683555987  8.393450e-01   0.99513393
## factor(Time_Period_ID)14           0.730801858  8.890822e-01   1.04736259
## factor(Time_Period_ID)15           0.781954795  9.345076e-01   1.08706033
## factor(Time_Period_ID)16           0.792023636  9.465946e-01   1.10116548
## factor(Time_Period_ID)17           0.871937760  1.029370e+00   1.18680201
## factor(Time_Period_ID)18           0.876755453  1.030412e+00   1.18406954
## factor(Time_Period_ID)19           0.846352674  1.016078e+00   1.18580255
## factor(Time_Period_ID)20           0.862723196  1.020809e+00   1.17889498
## factor(Time_Period_ID)21           0.902948056  1.056862e+00   1.21077529
## factor(Time_Period_ID)22           0.864848395  1.023971e+00   1.18309393
## factor(Time_Period_ID)23           1.012982576  1.169317e+00   1.32565133
## factor(Time_Period_ID)24           1.002680392  1.162103e+00   1.32152554
## factor(Time_Period_ID)25           0.995257127  1.156757e+00   1.31825610
## factor(Time_Period_ID)26           0.998867395  1.159892e+00   1.32091599
## factor(Time_Period_ID)27           1.096272192  1.255040e+00   1.41380696
## factor(Time_Period_ID)28           1.064983223  1.224102e+00   1.38322132
## factor(Time_Period_ID)29           1.115437722  1.275260e+00   1.43508298
## factor(Time_Period_ID)30           1.122689703  1.282527e+00   1.44236405
## factor(Time_Period_ID)31           1.221448699  1.384571e+00   1.54769345
## factor(Time_Period_ID)32           1.247870688  1.414272e+00   1.58067383
## factor(Time_Period_ID)33           1.382490763  1.554408e+00   1.72632572
## factor(Time_Period_ID)34           1.405897173  1.582829e+00   1.75976183
## factor(Time_Period_ID)35           1.452521096  1.635433e+00   1.81834407
## factor(Time_Period_ID)36           1.462387545  1.643334e+00   1.82427984
## factor(Time_Period_ID)37           1.440588652  1.621393e+00   1.80219655
## factor(Time_Period_ID)38           1.412883856  1.593328e+00   1.77377281
## factor(Time_Period_ID)39           1.444375280  1.624170e+00   1.80396544
## factor(Time_Period_ID)40           1.505345068  1.683371e+00   1.86139770
## Naloxone_Pharmacy_Yes_Redefined   -0.129703304 -5.661790e-02   0.01646751
## Naloxone_Pharmacy_No_Redefined    -0.030506735  3.658799e-02   0.10368272
## Medical_Marijuana_Redefined        0.199087446  2.777546e-01   0.35642174
## Recreational_Marijuana_Redefined  -0.346991479 -2.535416e-01  -0.16009181
## GSL_Redefined                     -0.011148894  4.494005e-02   0.10102899
## PDMP_Redefined                    -0.209301431 -1.514128e-01  -0.09352425
## Medicaid_Expansion_Redefined       0.039170120  9.274003e-02   0.14630994
## Intervention_Redefined            -0.073425116 -2.813085e-02   0.01716341
##                                     sd_coef
## (Intercept)                      0.07575327
## StateAlaska                      0.07172769
## StateArizona                     0.06420650
## StateArkansas                    0.05835211
## StateCalifornia                  0.06897075
## StateColorado                    0.06277320
## StateConnecticut                 0.06285123
## StateDelaware                    0.06070181
## StateFlorida                     0.05323621
## StateGeorgia                     0.04316293
## StateHawaii                      0.06077735
## StateIdaho                       0.04912707
## StateIllinois                    0.05835190
## StateIndiana                     0.05791328
## StateIowa                        0.05064497
## StateKansas                      0.04776005
## StateKentucky                    0.04337366
## StateLouisiana                   0.04616605
## StateMaine                       0.07330672
## StateMaryland                    0.10136572
## StateMassachusetts               0.12641775
## StateMichigan                    0.04738182
## StateMinnesota                   0.05350246
## StateMississippi                 0.04677974
## StateMissouri                    0.04652266
## StateMontana                     0.06829527
## StateNebraska                    0.05110210
## StateNevada                      0.07107811
## StateNew Hampshire               0.05728547
## StateNew Jersey                  0.07775100
## StateNew Mexico                  0.08779294
## StateNew York                    0.05091444
## StateNorth Carolina              0.03955435
## StateNorth Dakota                0.07819094
## StateOhio                        0.05211996
## StateOklahoma                    0.05788393
## StateOregon                      0.06315242
## StatePennsylvania                0.04361035
## StateRhode Island                0.16835068
## StateSouth Carolina              0.04348373
## StateSouth Dakota                0.06462029
## StateTennessee                   0.04089273
## StateTexas                       0.05606694
## StateUtah                        0.06871478
## StateVermont                     0.06653778
## StateVirginia                    0.04687284
## StateWashington                  0.06876793
## StateWest Virginia               0.07095006
## StateWisconsin                   0.04276741
## StateWyoming                     0.06013217
## factor(Time_Period_ID)2          0.09106656
## factor(Time_Period_ID)3          0.08536155
## factor(Time_Period_ID)4          0.08677965
## factor(Time_Period_ID)5          0.09361903
## factor(Time_Period_ID)6          0.09260369
## factor(Time_Period_ID)7          0.08468829
## factor(Time_Period_ID)8          0.08823745
## factor(Time_Period_ID)9          0.09254886
## factor(Time_Period_ID)10         0.09087371
## factor(Time_Period_ID)11         0.07923267
## factor(Time_Period_ID)12         0.08347359
## factor(Time_Period_ID)13         0.07948417
## factor(Time_Period_ID)14         0.08075529
## factor(Time_Period_ID)15         0.07783304
## factor(Time_Period_ID)16         0.07886272
## factor(Time_Period_ID)17         0.08032251
## factor(Time_Period_ID)18         0.07839645
## factor(Time_Period_ID)19         0.08659436
## factor(Time_Period_ID)20         0.08065607
## factor(Time_Period_ID)21         0.07852736
## factor(Time_Period_ID)22         0.08118509
## factor(Time_Period_ID)23         0.07976244
## factor(Time_Period_ID)24         0.08133805
## factor(Time_Period_ID)25         0.08239770
## factor(Time_Period_ID)26         0.08215525
## factor(Time_Period_ID)27         0.08100377
## factor(Time_Period_ID)28         0.08118319
## factor(Time_Period_ID)29         0.08154216
## factor(Time_Period_ID)30         0.08154958
## factor(Time_Period_ID)31         0.08322570
## factor(Time_Period_ID)32         0.08489876
## factor(Time_Period_ID)33         0.08771300
## factor(Time_Period_ID)34         0.09027160
## factor(Time_Period_ID)35         0.09332219
## factor(Time_Period_ID)36         0.09231946
## factor(Time_Period_ID)37         0.09224691
## factor(Time_Period_ID)38         0.09206351
## factor(Time_Period_ID)39         0.09173218
## factor(Time_Period_ID)40         0.09082975
## Naloxone_Pharmacy_Yes_Redefined  0.03728847
## Naloxone_Pharmacy_No_Redefined   0.03423200
## Medical_Marijuana_Redefined      0.04013630
## Recreational_Marijuana_Redefined 0.04767849
## GSL_Redefined                    0.02861681
## PDMP_Redefined                   0.02953499
## Medicaid_Expansion_Redefined     0.02733159
## Intervention_Redefined           0.02310932

8.2 Event Study

8.2.1 Model Fitting

#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures, 
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention

formula_event_study_log_fixed_time <- formula(paste("log(prop_dead) ~ State +
                                           factor(Time_Period_ID)  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2), 
                                            function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
                                     "+",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_log_fixed_time<-lm(formula_event_study_log_fixed_time,
                                         data = sensitivity_anlys_event_study_data)

summary(sensitivity_anlys_event_study_model_log_fixed_time)
## 
## Call:
## lm(formula = formula_event_study_log_fixed_time, data = sensitivity_anlys_event_study_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.02228 -0.14569  0.01955  0.15652  0.95435 
## 
## Coefficients:
##                                    Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -1.053e+01  9.794e-02 -107.541  < 2e-16 ***
## StateAlaska                       2.324e-01  1.026e-01    2.266 0.023563 *  
## StateArizona                      3.166e-01  8.008e-02    3.954 7.99e-05 ***
## StateArkansas                    -4.549e-01  7.537e-02   -6.035 1.92e-09 ***
## StateCalifornia                  -2.766e-01  9.149e-02   -3.024 0.002530 ** 
## StateColorado                     6.168e-02  8.383e-02    0.736 0.461975    
## StateConnecticut                  1.703e-01  7.466e-02    2.281 0.022668 *  
## StateDelaware                     2.950e-01  9.852e-02    2.995 0.002786 ** 
## StateFlorida                      2.413e-01  9.039e-02    2.669 0.007667 ** 
## StateGeorgia                     -5.729e-02  9.630e-02   -0.595 0.551977    
## StateHawaii                      -4.811e-01  9.031e-02   -5.327 1.12e-07 ***
## StateIdaho                       -5.384e-03  9.329e-02   -0.058 0.953986    
## StateIllinois                     7.740e-02  8.327e-02    0.930 0.352705    
## StateIndiana                      1.164e-01  7.200e-02    1.617 0.106035    
## StateIowa                        -7.084e-01  7.636e-02   -9.276  < 2e-16 ***
## StateKansas                      -2.353e-01  7.001e-02   -3.361 0.000792 ***
## StateKentucky                     7.580e-01  7.603e-02    9.970  < 2e-16 ***
## StateLouisiana                    3.007e-01  7.715e-02    3.897 0.000101 ***
## StateMaine                        4.097e-02  7.880e-02    0.520 0.603168    
## StateMaryland                    -1.605e+00  8.451e-02  -18.996  < 2e-16 ***
## StateMassachusetts               -9.130e-02  7.104e-02   -1.285 0.198864    
## StateMichigan                    -4.462e-02  7.448e-02   -0.599 0.549138    
## StateMinnesota                   -7.228e-01  7.345e-02   -9.841  < 2e-16 ***
## StateMississippi                  5.152e-02  8.710e-02    0.591 0.554306    
## StateMissouri                     1.271e-01  7.561e-02    1.681 0.092868 .  
## StateMontana                     -5.442e-01  8.034e-02   -6.774 1.69e-11 ***
## StateNebraska                    -8.068e-01  8.092e-02   -9.971  < 2e-16 ***
## StateNevada                       3.921e-01  7.723e-02    5.077 4.22e-07 ***
## StateNew Hampshire                1.404e-01  7.249e-02    1.937 0.052925 .  
## StateNew Jersey                  -2.221e-02  8.412e-02   -0.264 0.791765    
## StateNew Mexico                   5.982e-01  7.845e-02    7.626 3.87e-14 ***
## StateNew York                    -1.791e-01  7.218e-02   -2.482 0.013165 *  
## StateNorth Carolina               2.069e-01  7.362e-02    2.811 0.004993 ** 
## StateNorth Dakota                -1.080e+00  8.050e-02  -13.414  < 2e-16 ***
## StateOhio                         3.845e-01  9.623e-02    3.996 6.69e-05 ***
## StateOklahoma                     5.114e-01  7.480e-02    6.838 1.09e-11 ***
## StateOregon                      -3.107e-01  7.876e-02   -3.945 8.29e-05 ***
## StatePennsylvania                 4.983e-01  8.998e-02    5.538 3.51e-08 ***
## StateRhode Island                -2.431e-01  8.873e-02   -2.739 0.006215 ** 
## StateSouth Carolina               3.253e-01  9.485e-02    3.429 0.000618 ***
## StateSouth Dakota                -9.065e-01  9.797e-02   -9.252  < 2e-16 ***
## StateTennessee                    4.699e-01  6.941e-02    6.769 1.74e-11 ***
## StateTexas                       -6.328e-02  8.721e-02   -0.726 0.468195    
## StateUtah                        -1.147e-01  7.245e-02   -1.584 0.113471    
## StateVermont                     -2.100e-01  7.455e-02   -2.816 0.004908 ** 
## StateVirginia                    -7.392e-02  7.836e-02   -0.943 0.345611    
## StateWashington                   6.118e-03  7.875e-02    0.078 0.938083    
## StateWest Virginia                8.577e-01  8.121e-02   10.562  < 2e-16 ***
## StateWisconsin                   -3.569e-02  7.727e-02   -0.462 0.644212    
## StateWyoming                      4.985e-03  7.093e-02    0.070 0.943980    
## factor(Time_Period_ID)2          -8.285e-03  6.408e-02   -0.129 0.897144    
## factor(Time_Period_ID)3           9.515e-02  6.476e-02    1.469 0.141941    
## factor(Time_Period_ID)4           1.316e-01  6.412e-02    2.052 0.040324 *  
## factor(Time_Period_ID)5           2.820e-01  6.545e-02    4.309 1.73e-05 ***
## factor(Time_Period_ID)6           2.904e-01  6.640e-02    4.374 1.29e-05 ***
## factor(Time_Period_ID)7           4.234e-01  6.702e-02    6.318 3.32e-10 ***
## factor(Time_Period_ID)8           3.970e-01  6.853e-02    5.792 8.16e-09 ***
## factor(Time_Period_ID)9           4.752e-01  6.989e-02    6.800 1.41e-11 ***
## factor(Time_Period_ID)10          4.632e-01  7.165e-02    6.465 1.30e-10 ***
## factor(Time_Period_ID)11          5.738e-01  7.352e-02    7.806 9.87e-15 ***
## factor(Time_Period_ID)12          5.842e-01  7.549e-02    7.740 1.64e-14 ***
## factor(Time_Period_ID)13          7.466e-01  7.760e-02    9.622  < 2e-16 ***
## factor(Time_Period_ID)14          7.828e-01  7.998e-02    9.788  < 2e-16 ***
## factor(Time_Period_ID)15          8.174e-01  8.218e-02    9.947  < 2e-16 ***
## factor(Time_Period_ID)16          8.321e-01  8.444e-02    9.854  < 2e-16 ***
## factor(Time_Period_ID)17          9.073e-01  8.736e-02   10.386  < 2e-16 ***
## factor(Time_Period_ID)18          9.009e-01  9.000e-02   10.010  < 2e-16 ***
## factor(Time_Period_ID)19          8.851e-01  9.260e-02    9.559  < 2e-16 ***
## factor(Time_Period_ID)20          8.812e-01  9.570e-02    9.208  < 2e-16 ***
## factor(Time_Period_ID)21          9.069e-01  9.865e-02    9.192  < 2e-16 ***
## factor(Time_Period_ID)22          8.747e-01  1.015e-01    8.616  < 2e-16 ***
## factor(Time_Period_ID)23          1.014e+00  1.047e-01    9.683  < 2e-16 ***
## factor(Time_Period_ID)24          1.007e+00  1.079e-01    9.335  < 2e-16 ***
## factor(Time_Period_ID)25          1.009e+00  1.110e-01    9.091  < 2e-16 ***
## factor(Time_Period_ID)26          1.004e+00  1.142e-01    8.791  < 2e-16 ***
## factor(Time_Period_ID)27          1.094e+00  1.174e-01    9.314  < 2e-16 ***
## factor(Time_Period_ID)28          1.059e+00  1.207e-01    8.777  < 2e-16 ***
## factor(Time_Period_ID)29          1.099e+00  1.255e-01    8.758  < 2e-16 ***
## factor(Time_Period_ID)30          1.107e+00  1.292e-01    8.566  < 2e-16 ***
## factor(Time_Period_ID)31          1.199e+00  1.328e-01    9.030  < 2e-16 ***
## factor(Time_Period_ID)32          1.221e+00  1.372e-01    8.904  < 2e-16 ***
## factor(Time_Period_ID)33          1.365e+00  1.413e-01    9.664  < 2e-16 ***
## factor(Time_Period_ID)34          1.381e+00  1.457e-01    9.481  < 2e-16 ***
## factor(Time_Period_ID)35          1.425e+00  1.490e-01    9.567  < 2e-16 ***
## factor(Time_Period_ID)36          1.440e+00  1.531e-01    9.403  < 2e-16 ***
## factor(Time_Period_ID)37          1.410e+00  1.565e-01    9.011  < 2e-16 ***
## factor(Time_Period_ID)38          1.383e+00  1.601e-01    8.636  < 2e-16 ***
## factor(Time_Period_ID)39          1.416e+00  1.639e-01    8.641  < 2e-16 ***
## factor(Time_Period_ID)40          1.474e+00  1.672e-01    8.818  < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined  -4.588e-02  4.649e-02   -0.987 0.323832    
## Naloxone_Pharmacy_No_Redefined    3.276e-02  3.960e-02    0.827 0.408289    
## Medical_Marijuana_Redefined       2.744e-01  3.157e-02    8.691  < 2e-16 ***
## Recreational_Marijuana_Redefined -2.668e-01  4.738e-02   -5.631 2.07e-08 ***
## GSL_Redefined                     5.450e-02  3.295e-02    1.654 0.098347 .  
## PDMP_Redefined                   -1.777e-01  2.646e-02   -6.717 2.47e-11 ***
## Medicaid_Expansion_Redefined      1.056e-01  3.257e-02    3.241 0.001212 ** 
## neg_2_pd                          2.842e-02  6.450e-02    0.441 0.659514    
## neg_3_pd                          4.588e-03  6.563e-02    0.070 0.944274    
## neg_4_pd                         -2.453e-02  6.646e-02   -0.369 0.712106    
## neg_5_pd                         -3.613e-02  6.734e-02   -0.536 0.591692    
## neg_6_pd                         -4.071e-02  6.962e-02   -0.585 0.558776    
## neg_7_pd                         -9.720e-02  7.055e-02   -1.378 0.168450    
## neg_8_pd                         -1.631e-01  7.233e-02   -2.255 0.024280 *  
## neg_9_pd                         -1.185e-01  7.515e-02   -1.577 0.114987    
## neg_10_pd                        -8.315e-02  7.745e-02   -1.074 0.283149    
## neg_11_pd                        -8.336e-02  7.989e-02   -1.043 0.296875    
## neg_12_pd                        -1.193e-02  8.433e-02   -0.141 0.887510    
## neg_13_pd                        -1.133e-01  8.638e-02   -1.312 0.189697    
## neg_14_pd                        -1.448e-01  8.865e-02   -1.634 0.102453    
## neg_15_pd                        -1.933e-01  9.074e-02   -2.130 0.033316 *  
## neg_16_pd                        -1.865e-01  9.492e-02   -1.965 0.049601 *  
## neg_17_pd                        -1.805e-01  1.010e-01   -1.787 0.074138 .  
## neg_18_pd                        -1.922e-01  1.043e-01   -1.843 0.065479 .  
## neg_19_pd                        -3.035e-01  1.075e-01   -2.824 0.004801 ** 
## neg_20_pd                        -3.790e-01  1.141e-01   -3.321 0.000913 ***
## neg_21_pd                        -3.025e-01  1.215e-01   -2.489 0.012889 *  
## neg_22_pd                        -2.874e-01  1.238e-01   -2.321 0.020378 *  
## neg_23_pd                        -2.988e-01  1.284e-01   -2.327 0.020098 *  
## neg_24_pd                        -3.796e-01  1.384e-01   -2.743 0.006139 ** 
## neg_25_pd                        -2.419e-01  1.407e-01   -1.719 0.085735 .  
## neg_26_pd                        -2.266e-01  1.463e-01   -1.549 0.121546    
## neg_27_pd                        -4.453e-01  1.631e-01   -2.730 0.006397 ** 
## neg_28_pd                        -4.520e-01  1.653e-01   -2.734 0.006314 ** 
## neg_29_pd                        -2.018e-01  1.750e-01   -1.153 0.249081    
## neg_30_pd                        -2.525e-01  1.868e-01   -1.351 0.176702    
## neg_31_pd                        -2.519e-01  1.890e-01   -1.333 0.182589    
## neg_32_pd                        -2.585e-01  2.040e-01   -1.267 0.205234    
## neg_33_pd                        -2.719e-01  2.593e-01   -1.049 0.294503    
## pos_0_pd                         -9.966e-05  6.423e-02   -0.002 0.998762    
## pos_1_pd                         -2.641e-02  6.490e-02   -0.407 0.684052    
## pos_2_pd                          2.020e-02  6.519e-02    0.310 0.756714    
## pos_3_pd                         -5.337e-03  6.644e-02   -0.080 0.935983    
## pos_4_pd                          1.567e-03  6.758e-02    0.023 0.981502    
## pos_5_pd                         -2.710e-02  6.895e-02   -0.393 0.694329    
## pos_6_pd                         -2.756e-02  7.086e-02   -0.389 0.697357    
## pos_7_pd                         -1.702e-02  7.268e-02   -0.234 0.814927    
## pos_8_pd                         -3.948e-02  7.555e-02   -0.523 0.601354    
## pos_9_pd                         -3.794e-02  7.803e-02   -0.486 0.626917    
## pos_10_pd                        -4.375e-02  8.001e-02   -0.547 0.584554    
## pos_11_pd                        -3.991e-02  8.275e-02   -0.482 0.629654    
## pos_12_pd                        -3.796e-02  8.559e-02   -0.444 0.657448    
## pos_13_pd                        -9.049e-02  8.808e-02   -1.027 0.304399    
## pos_14_pd                        -6.580e-02  9.171e-02   -0.718 0.473133    
## pos_15_pd                        -5.502e-02  9.511e-02   -0.578 0.563026    
## pos_16_pd                        -5.159e-02  9.785e-02   -0.527 0.598071    
## pos_17_pd                        -2.880e-02  1.018e-01   -0.283 0.777418    
## pos_18_pd                         1.626e-02  1.054e-01    0.154 0.877433    
## pos_19_pd                         2.997e-02  1.080e-01    0.277 0.781506    
## pos_20_pd                         4.163e-02  1.124e-01    0.370 0.711258    
## pos_21_pd                         2.602e-02  1.170e-01    0.222 0.824030    
## pos_22_pd                         2.513e-02  1.206e-01    0.208 0.834909    
## pos_23_pd                         1.943e-02  1.245e-01    0.156 0.875987    
## pos_24_pd                        -3.386e-02  1.305e-01   -0.259 0.795310    
## pos_25_pd                         5.876e-03  1.361e-01    0.043 0.965569    
## pos_26_pd                         2.342e-02  1.393e-01    0.168 0.866536    
## pos_27_pd                        -1.540e-02  1.428e-01   -0.108 0.914141    
## pos_28_pd                         1.567e-02  1.458e-01    0.107 0.914462    
## pos_29_pd                         3.032e-02  1.537e-01    0.197 0.843615    
## pos_30_pd                         8.008e-02  1.583e-01    0.506 0.613054    
## pos_31_pd                         1.375e-01  1.636e-01    0.841 0.400626    
## pos_32_pd                         1.034e-01  1.739e-01    0.594 0.552267    
## pos_33_pd                         9.727e-02  1.807e-01    0.538 0.590467    
## pos_34_pd                         1.147e-01  1.839e-01    0.624 0.532921    
## pos_35_pd                        -6.920e-02  2.018e-01   -0.343 0.731649    
## pos_36_pd                        -9.751e-02  2.047e-01   -0.476 0.633885    
## pos_37_pd                        -5.381e-02  2.280e-01   -0.236 0.813430    
## pos_38_pd                        -1.618e-02  2.809e-01   -0.058 0.954054    
## pos_39_pd                        -7.100e-02  2.832e-01   -0.251 0.802039    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3099 on 1832 degrees of freedom
## Multiple R-squared:  0.8363, Adjusted R-squared:  0.8213 
## F-statistic: 56.03 on 167 and 1832 DF,  p-value: < 2.2e-16

8.2.2 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_time <- model.matrix(sensitivity_anlys_event_study_model_log_fixed_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_log_fixed_time <- coef(sensitivity_anlys_event_study_model_log_fixed_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_log_fixed_time <- 
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_time), 
                                                             log(sensitivity_anlys_event_study_data$prop_dead),
                                                             coefficient_values_sensitivity_anlys_event_study_log_fixed_time, 
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_log_fixed_time)
##                                        lb_coef   coef_values       ub_coef
## (Intercept)                      -10.729822917 -1.053284e+01 -10.335859558
## StateAlaska                        0.054172688  2.323927e-01   0.410612739
## StateArizona                       0.170267751  3.166173e-01   0.462966918
## StateArkansas                     -0.568347675 -4.548515e-01  -0.341355289
## StateCalifornia                   -0.432485956 -2.766479e-01  -0.120809850
## StateColorado                     -0.074937939  6.167797e-02   0.198293878
## StateConnecticut                   0.044472662  1.702845e-01   0.296096305
## StateDelaware                      0.141709808  2.950337e-01   0.448357616
## StateFlorida                       0.107469795  2.412924e-01   0.375114923
## StateGeorgia                      -0.190014286 -5.729004e-02   0.075434201
## StateHawaii                       -0.620522703 -4.811223e-01  -0.341721945
## StateIdaho                        -0.151413956 -5.383928e-03   0.140646099
## StateIllinois                     -0.052536841  7.740347e-02   0.207343782
## StateIndiana                       0.004043564  1.164288e-01   0.228813986
## StateIowa                         -0.830486766 -7.083535e-01  -0.586220323
## StateKansas                       -0.332741287 -2.353032e-01  -0.137865208
## StateKentucky                      0.660051210  7.580209e-01   0.855990600
## StateLouisiana                     0.193327284  3.006912e-01   0.408055106
## StateMaine                        -0.110790892  4.096916e-02   0.192729208
## StateMaryland                     -1.820581271 -1.605356e+00  -1.390130259
## StateMassachusetts                -0.340760428 -9.130156e-02   0.158157304
## StateMichigan                     -0.143557790 -4.462401e-02   0.054309774
## StateMinnesota                    -0.834357418 -7.228330e-01  -0.611308554
## StateMississippi                  -0.083209611  5.151543e-02   0.186240462
## StateMissouri                      0.022281284  1.271294e-01   0.231977592
## StateMontana                      -0.683838462 -5.441789e-01  -0.404519244
## StateNebraska                     -0.922594757 -8.068464e-01  -0.691098116
## StateNevada                        0.249787292  3.921379e-01   0.534488518
## StateNew Hampshire                 0.021838627  1.403922e-01   0.258945830
## StateNew Jersey                   -0.185139897 -2.221187e-02   0.140716152
## StateNew Mexico                    0.415847614  5.982206e-01   0.780593579
## StateNew York                     -0.281543924 -1.791234e-01  -0.076702829
## StateNorth Carolina                0.117383420  2.069288e-01   0.296474120
## StateNorth Dakota                 -1.248935424 -1.079797e+00  -0.910658399
## StateOhio                          0.230727211  3.845419e-01   0.538356685
## StateOklahoma                      0.389192360  5.114345e-01   0.633676641
## StateOregon                       -0.438805257 -3.106916e-01  -0.182577884
## StatePennsylvania                  0.377698079  4.982749e-01   0.618851700
## StateRhode Island                 -0.551525979 -2.430720e-01   0.065382040
## StateSouth Carolina                0.189968848  3.252890e-01   0.460609145
## StateSouth Dakota                 -1.074149221 -9.064547e-01  -0.738760186
## StateTennessee                     0.383632643  4.698579e-01   0.556083105
## StateTexas                        -0.195105528 -6.327772e-02   0.068550094
## StateUtah                         -0.264457420 -1.147339e-01   0.034989521
## StateVermont                      -0.344753613 -2.099737e-01  -0.075193713
## StateVirginia                     -0.178738571 -7.392103e-02   0.030896511
## StateWashington                   -0.131596796  6.117690e-03   0.143832176
## StateWest Virginia                 0.709111451  8.576940e-01   1.006276620
## StateWisconsin                    -0.141909582 -3.569278e-02   0.070524014
## StateWyoming                      -0.114418061  4.984789e-03   0.124387638
## factor(Time_Period_ID)2           -0.185613676 -8.284615e-03   0.169044446
## factor(Time_Period_ID)3           -0.077695631  9.515333e-02   0.268002288
## factor(Time_Period_ID)4           -0.039995457  1.315751e-01   0.303145756
## factor(Time_Period_ID)5            0.093433280  2.820032e-01   0.470573215
## factor(Time_Period_ID)6            0.093280044  2.904193e-01   0.487558603
## factor(Time_Period_ID)7            0.252091912  4.234193e-01   0.594746691
## factor(Time_Period_ID)8            0.222405605  3.969617e-01   0.571517781
## factor(Time_Period_ID)9            0.286735480  4.752227e-01   0.663710011
## factor(Time_Period_ID)10           0.274963928  4.631810e-01   0.651398129
## factor(Time_Period_ID)11           0.409700937  5.738495e-01   0.737998069
## factor(Time_Period_ID)12           0.413066294  5.842444e-01   0.755422509
## factor(Time_Period_ID)13           0.579991122  7.466213e-01   0.913251427
## factor(Time_Period_ID)14           0.610574663  7.828297e-01   0.955084712
## factor(Time_Period_ID)15           0.650812359  8.174001e-01   0.983987888
## factor(Time_Period_ID)16           0.661875743  8.321066e-01   1.002337412
## factor(Time_Period_ID)17           0.731882165  9.073307e-01   1.082779285
## factor(Time_Period_ID)18           0.726252701  9.008909e-01   1.075529002
## factor(Time_Period_ID)19           0.694999680  8.851166e-01   1.075233610
## factor(Time_Period_ID)20           0.696926890  8.811826e-01   1.065438407
## factor(Time_Period_ID)21           0.723505825  9.068531e-01   1.090200277
## factor(Time_Period_ID)22           0.683822472  8.747203e-01   1.065618097
## factor(Time_Period_ID)23           0.822566173  1.013657e+00   1.204748514
## factor(Time_Period_ID)24           0.810315411  1.007054e+00   1.203793339
## factor(Time_Period_ID)25           0.807181835  1.008954e+00   1.210725522
## factor(Time_Period_ID)26           0.797761118  1.003976e+00   1.210191767
## factor(Time_Period_ID)27           0.887253689  1.093706e+00   1.300158380
## factor(Time_Period_ID)28           0.847506641  1.059129e+00   1.270750477
## factor(Time_Period_ID)29           0.881240671  1.099261e+00   1.317280687
## factor(Time_Period_ID)30           0.883986738  1.106560e+00   1.329134253
## factor(Time_Period_ID)31           0.970227722  1.198997e+00   1.427765817
## factor(Time_Period_ID)32           0.987364421  1.221435e+00   1.455505258
## factor(Time_Period_ID)33           1.124281297  1.365204e+00   1.606125890
## factor(Time_Period_ID)34           1.133100986  1.381331e+00   1.629561886
## factor(Time_Period_ID)35           1.166984332  1.425255e+00   1.683525341
## factor(Time_Period_ID)36           1.179270897  1.439727e+00   1.700182625
## factor(Time_Period_ID)37           1.145827343  1.410226e+00   1.674623837
## factor(Time_Period_ID)38           1.113581095  1.382541e+00   1.651501622
## factor(Time_Period_ID)39           1.143068642  1.415995e+00   1.688922118
## factor(Time_Period_ID)40           1.198384668  1.474234e+00   1.750083268
## Naloxone_Pharmacy_Yes_Redefined   -0.119376311 -4.588103e-02   0.027614254
## Naloxone_Pharmacy_No_Redefined    -0.036005115  3.275524e-02   0.101515586
## Medical_Marijuana_Redefined        0.194971756  2.744189e-01   0.353866106
## Recreational_Marijuana_Redefined  -0.362989288 -2.668305e-01  -0.170671766
## GSL_Redefined                     -0.003413345  5.449834e-02   0.112410016
## PDMP_Redefined                    -0.238570986 -1.777134e-01  -0.116855721
## Medicaid_Expansion_Redefined       0.049972645  1.055728e-01   0.161172955
## neg_2_pd                          -0.082381838  2.842348e-02   0.139228801
## neg_3_pd                          -0.110294880  4.588085e-03   0.119471050
## neg_4_pd                          -0.143934103 -2.452977e-02   0.094874563
## neg_5_pd                          -0.152141932 -3.612539e-02   0.079891152
## neg_6_pd                          -0.157291283 -4.071050e-02   0.075870277
## neg_7_pd                          -0.216961288 -9.720499e-02   0.022551303
## neg_8_pd                          -0.311300104 -1.630612e-01  -0.014822393
## neg_9_pd                          -0.277368199 -1.185041e-01   0.040359925
## neg_10_pd                         -0.231863683 -8.314656e-02   0.065570568
## neg_11_pd                         -0.241548942 -8.335927e-02   0.074830405
## neg_12_pd                         -0.187872406 -1.193000e-02   0.164012406
## neg_13_pd                         -0.292118767 -1.133316e-01   0.065455479
## neg_14_pd                         -0.322018833 -1.448378e-01   0.032343181
## neg_15_pd                         -0.401176261 -1.932577e-01   0.014660903
## neg_16_pd                         -0.387587796 -1.864842e-01   0.014619443
## neg_17_pd                         -0.365468925 -1.805327e-01   0.004403501
## neg_18_pd                         -0.371454398 -1.921785e-01  -0.012902518
## neg_19_pd                         -0.573235279 -3.035347e-01  -0.033834048
## neg_20_pd                         -0.692949454 -3.789875e-01  -0.065025477
## neg_21_pd                         -0.537832807 -3.024593e-01  -0.067085797
## neg_22_pd                         -0.540851052 -2.873767e-01  -0.033902419
## neg_23_pd                         -0.640613094 -2.987530e-01   0.043107028
## neg_24_pd                         -0.789721271 -3.795698e-01   0.030581669
## neg_25_pd                         -0.578611412 -2.419419e-01   0.094727623
## neg_26_pd                         -0.618467889 -2.266129e-01   0.165242179
## neg_27_pd                         -1.010215002 -4.452797e-01   0.119655644
## neg_28_pd                         -1.025870029 -4.520347e-01   0.121800545
## neg_29_pd                         -0.581810980 -2.018027e-01   0.178205608
## neg_30_pd                         -0.603349715 -2.525073e-01   0.098335102
## neg_31_pd                         -0.533605111 -2.519349e-01   0.029735393
## neg_32_pd                         -0.568068910 -2.584989e-01   0.051071072
## neg_33_pd                         -0.640899674 -2.718532e-01   0.097193207
## pos_0_pd                          -0.106009954 -9.965934e-05   0.105810635
## pos_1_pd                          -0.141197407 -2.641429e-02   0.088368817
## pos_2_pd                          -0.084217175  2.019822e-02   0.124613608
## pos_3_pd                          -0.111115132 -5.336848e-03   0.100441435
## pos_4_pd                          -0.106262518  1.567118e-03   0.109396755
## pos_5_pd                          -0.135836515 -2.710068e-02   0.081635154
## pos_6_pd                          -0.140323601 -2.755982e-02   0.085203971
## pos_7_pd                          -0.135286509 -1.701538e-02   0.101255742
## pos_8_pd                          -0.152867258 -3.947891e-02   0.073909438
## pos_9_pd                          -0.160141919 -3.793528e-02   0.084271362
## pos_10_pd                         -0.171398614 -4.375081e-02   0.083896986
## pos_11_pd                         -0.159818092 -3.991163e-02   0.079994835
## pos_12_pd                         -0.162396258 -3.795940e-02   0.086477456
## pos_13_pd                         -0.232035112 -9.049109e-02   0.051052937
## pos_14_pd                         -0.210024781 -6.580435e-02   0.078416078
## pos_15_pd                         -0.202962942 -5.501595e-02   0.092931033
## pos_16_pd                         -0.202208346 -5.159255e-02   0.099023236
## pos_17_pd                         -0.190587955 -2.879518e-02   0.132997597
## pos_18_pd                         -0.148561848  1.625955e-02   0.181080958
## pos_19_pd                         -0.128156389  2.996664e-02   0.188089663
## pos_20_pd                         -0.125065171  4.162673e-02   0.208318630
## pos_21_pd                         -0.149339949  2.602476e-02   0.201389466
## pos_22_pd                         -0.150137811  2.513029e-02   0.200398384
## pos_23_pd                         -0.160747281  1.942726e-02   0.199601797
## pos_24_pd                         -0.219782680 -3.385570e-02   0.152071285
## pos_25_pd                         -0.197009528  5.876321e-03   0.208762170
## pos_26_pd                         -0.179446782  2.341892e-02   0.226284623
## pos_27_pd                         -0.238902512 -1.540153e-02   0.208099451
## pos_28_pd                         -0.211932620  1.566547e-02   0.243263562
## pos_29_pd                         -0.217174774  3.031926e-02   0.277813301
## pos_30_pd                         -0.176984121  8.008246e-02   0.337149044
## pos_31_pd                         -0.143971113  1.375114e-01   0.418994004
## pos_32_pd                         -0.178568702  1.033884e-01   0.385345418
## pos_33_pd                         -0.220811762  9.727439e-02   0.415360537
## pos_34_pd                         -0.200288717  1.146659e-01   0.429620443
## pos_35_pd                         -0.337731577 -6.920026e-02   0.199331055
## pos_36_pd                         -0.360359328 -9.750608e-02   0.165347160
## pos_37_pd                         -0.321532694 -5.381403e-02   0.213904627
## pos_38_pd                         -0.300410958 -1.618438e-02   0.268042190
## pos_39_pd                         -0.421317872 -7.100497e-02   0.279307923
##                                     sd_coef
## (Intercept)                      0.10050086
## StateAlaska                      0.09092858
## StateArizona                     0.07466815
## StateArkansas                    0.05790622
## StateCalifornia                  0.07950921
## StateColorado                    0.06970199
## StateConnecticut                 0.06418971
## StateDelaware                    0.07822648
## StateFlorida                     0.06827682
## StateGeorgia                     0.06771645
## StateHawaii                      0.07112264
## StateIdaho                       0.07450512
## StateIllinois                    0.06629608
## StateIndiana                     0.05733939
## StateIowa                        0.06231287
## StateKansas                      0.04971329
## StateKentucky                    0.04998454
## StateLouisiana                   0.05477751
## StateMaine                       0.07742860
## StateMaryland                    0.10980893
## StateMassachusetts               0.12727493
## StateMichigan                    0.05047642
## StateMinnesota                   0.05690022
## StateMississippi                 0.06873726
## StateMissouri                    0.05349396
## StateMontana                     0.07125490
## StateNebraska                    0.05905527
## StateNevada                      0.07262786
## StateNew Hampshire               0.06048653
## StateNew Jersey                  0.08312654
## StateNew Mexico                  0.09304744
## StateNew York                    0.05225538
## StateNorth Carolina              0.04568640
## StateNorth Dakota                0.08629516
## StateOhio                        0.07847691
## StateOklahoma                    0.06236844
## StateOregon                      0.06536413
## StatePennsylvania                0.06151878
## StateRhode Island                0.15737449
## StateSouth Carolina              0.06904089
## StateSouth Dakota                0.08555843
## StateTennessee                   0.04399246
## StateTexas                       0.06725909
## StateUtah                        0.07638953
## StateVermont                     0.06876528
## StateVirginia                    0.05347834
## StateWashington                  0.07026249
## StateWest Virginia               0.07580744
## StateWisconsin                   0.05419224
## StateWyoming                     0.06091982
## factor(Time_Period_ID)2          0.09047401
## factor(Time_Period_ID)3          0.08818824
## factor(Time_Period_ID)4          0.08753602
## factor(Time_Period_ID)5          0.09620917
## factor(Time_Period_ID)6          0.10058126
## factor(Time_Period_ID)7          0.08741193
## factor(Time_Period_ID)8          0.08905923
## factor(Time_Period_ID)9          0.09616697
## factor(Time_Period_ID)10         0.09602913
## factor(Time_Period_ID)11         0.08374927
## factor(Time_Period_ID)12         0.08733577
## factor(Time_Period_ID)13         0.08501538
## factor(Time_Period_ID)14         0.08788522
## factor(Time_Period_ID)15         0.08499376
## factor(Time_Period_ID)16         0.08685247
## factor(Time_Period_ID)17         0.08951457
## factor(Time_Period_ID)18         0.08910110
## factor(Time_Period_ID)19         0.09699845
## factor(Time_Period_ID)20         0.09400804
## factor(Time_Period_ID)21         0.09354450
## factor(Time_Period_ID)22         0.09739684
## factor(Time_Period_ID)23         0.09749550
## factor(Time_Period_ID)24         0.10037702
## factor(Time_Period_ID)25         0.10294482
## factor(Time_Period_ID)26         0.10521190
## factor(Time_Period_ID)27         0.10533283
## factor(Time_Period_ID)28         0.10797037
## factor(Time_Period_ID)29         0.11123470
## factor(Time_Period_ID)30         0.11355804
## factor(Time_Period_ID)31         0.11671890
## factor(Time_Period_ID)32         0.11942368
## factor(Time_Period_ID)33         0.12291954
## factor(Time_Period_ID)34         0.12664819
## factor(Time_Period_ID)35         0.13177067
## factor(Time_Period_ID)36         0.13288564
## factor(Time_Period_ID)37         0.13489706
## factor(Time_Period_ID)38         0.13722462
## factor(Time_Period_ID)39         0.13924834
## factor(Time_Period_ID)40         0.14073944
## Naloxone_Pharmacy_Yes_Redefined  0.03749759
## Naloxone_Pharmacy_No_Redefined   0.03508181
## Medical_Marijuana_Redefined      0.04053427
## Recreational_Marijuana_Redefined 0.04906059
## GSL_Redefined                    0.02954678
## PDMP_Redefined                   0.03104981
## Medicaid_Expansion_Redefined     0.02836743
## neg_2_pd                         0.05653333
## neg_3_pd                         0.05861376
## neg_4_pd                         0.06092058
## neg_5_pd                         0.05919211
## neg_6_pd                         0.05947999
## neg_7_pd                         0.06110015
## neg_8_pd                         0.07563207
## neg_9_pd                         0.08105309
## neg_10_pd                        0.07587608
## neg_11_pd                        0.08070902
## neg_12_pd                        0.08976653
## neg_13_pd                        0.09121792
## neg_14_pd                        0.09039847
## neg_15_pd                        0.10608091
## neg_16_pd                        0.10260389
## neg_17_pd                        0.09435521
## neg_18_pd                        0.09146732
## neg_19_pd                        0.13760235
## neg_20_pd                        0.16018469
## neg_21_pd                        0.12008852
## neg_22_pd                        0.12932363
## neg_23_pd                        0.17441840
## neg_24_pd                        0.20926095
## neg_25_pd                        0.17177016
## neg_26_pd                        0.19992604
## neg_27_pd                        0.28823231
## neg_28_pd                        0.29277311
## neg_29_pd                        0.19388178
## neg_30_pd                        0.17900123
## neg_31_pd                        0.14370931
## neg_32_pd                        0.15794387
## neg_33_pd                        0.18828900
## pos_0_pd                         0.05403586
## pos_1_pd                         0.05856281
## pos_2_pd                         0.05327316
## pos_3_pd                         0.05396851
## pos_4_pd                         0.05501512
## pos_5_pd                         0.05547747
## pos_6_pd                         0.05753254
## pos_7_pd                         0.06034241
## pos_8_pd                         0.05785120
## pos_9_pd                         0.06235033
## pos_10_pd                        0.06512643
## pos_11_pd                        0.06117677
## pos_12_pd                        0.06348819
## pos_13_pd                        0.07221634
## pos_14_pd                        0.07358185
## pos_15_pd                        0.07548316
## pos_16_pd                        0.07684479
## pos_17_pd                        0.08254733
## pos_18_pd                        0.08409255
## pos_19_pd                        0.08067501
## pos_20_pd                        0.08504689
## pos_21_pd                        0.08947179
## pos_22_pd                        0.08942250
## pos_23_pd                        0.09192579
## pos_24_pd                        0.09486071
## pos_25_pd                        0.10351319
## pos_26_pd                        0.10350291
## pos_27_pd                        0.11403111
## pos_28_pd                        0.11612148
## pos_29_pd                        0.12627247
## pos_30_pd                        0.13115642
## pos_31_pd                        0.14361355
## pos_32_pd                        0.14385564
## pos_33_pd                        0.16228885
## pos_34_pd                        0.16069111
## pos_35_pd                        0.13700577
## pos_36_pd                        0.13410880
## pos_37_pd                        0.13659115
## pos_38_pd                        0.14501356
## pos_39_pd                        0.17873107
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")

8.2.3 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_fixed_time <- sensitivity_anlys_event_study_sd_and_ci_log_fixed_time %>%
  mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_log_fixed_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study_log_fixed_time, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

8.3 Analysis With Only Periods After Treatment

formula_post_tx_log_fixed_time <- formula(paste("log(prop_dead)~ State +
                                           factor(Time_Period_ID)  +
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_fixed_time<-lm(formula_post_tx_log_fixed_time,
                                         data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_log_fixed_time)
## 
## Call:
## lm(formula = formula_post_tx_log_fixed_time, data = sensitivity_anlys_event_study_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.10074 -0.14327  0.01533  0.15938  0.94853 
## 
## Coefficients:
##                                    Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                      -10.702051   0.066574 -160.754  < 2e-16 ***
## StateAlaska                        0.031180   0.079305    0.393 0.694238    
## StateArizona                       0.200914   0.072119    2.786 0.005392 ** 
## StateArkansas                     -0.539628   0.071000   -7.600 4.65e-14 ***
## StateCalifornia                   -0.142773   0.080171   -1.781 0.075100 .  
## StateColorado                     -0.041236   0.077986   -0.529 0.597036    
## StateConnecticut                   0.171073   0.074642    2.292 0.022021 *  
## StateDelaware                      0.096475   0.073288    1.316 0.188207    
## StateFlorida                       0.400005   0.074168    5.393 7.80e-08 ***
## StateGeorgia                       0.125678   0.075840    1.657 0.097657 .  
## StateHawaii                       -0.546050   0.078391   -6.966 4.51e-12 ***
## StateIdaho                        -0.191458   0.071702   -2.670 0.007647 ** 
## StateIllinois                      0.197690   0.073388    2.694 0.007128 ** 
## StateIndiana                       0.064618   0.070335    0.919 0.358360    
## StateIowa                         -0.627597   0.071207   -8.814  < 2e-16 ***
## StateKansas                       -0.221516   0.069868   -3.170 0.001547 ** 
## StateKentucky                      0.667804   0.071064    9.397  < 2e-16 ***
## StateLouisiana                     0.391731   0.070770    5.535 3.55e-08 ***
## StateMaine                         0.002399   0.077764    0.031 0.975393    
## StateMaryland                     -1.476507   0.073289  -20.146  < 2e-16 ***
## StateMassachusetts                -0.097092   0.071028   -1.367 0.171806    
## StateMichigan                      0.002758   0.072547    0.038 0.969681    
## StateMinnesota                    -0.713219   0.073347   -9.724  < 2e-16 ***
## StateMississippi                  -0.112658   0.070845   -1.590 0.111959    
## StateMissouri                      0.190079   0.072468    2.623 0.008788 ** 
## StateMontana                      -0.459116   0.074860   -6.133 1.05e-09 ***
## StateNebraska                     -0.928373   0.071698  -12.948  < 2e-16 ***
## StateNevada                        0.433983   0.075705    5.733 1.15e-08 ***
## StateNew Hampshire                 0.092263   0.071080    1.298 0.194442    
## StateNew Jersey                    0.103757   0.073357    1.414 0.157408    
## StateNew Mexico                    0.539876   0.076524    7.055 2.42e-12 ***
## StateNew York                     -0.171359   0.072121   -2.376 0.017602 *  
## StateNorth Carolina                0.271801   0.070129    3.876 0.000110 ***
## StateNorth Dakota                 -1.202645   0.071009  -16.936  < 2e-16 ***
## StateOhio                          0.565722   0.076102    7.434 1.60e-13 ***
## StateOklahoma                      0.428515   0.070576    6.072 1.53e-09 ***
## StateOregon                       -0.356845   0.077387   -4.611 4.28e-06 ***
## StatePennsylvania                  0.653720   0.074362    8.791  < 2e-16 ***
## StateRhode Island                 -0.407196   0.074006   -5.502 4.27e-08 ***
## StateSouth Carolina                0.134528   0.071476    1.882 0.059972 .  
## StateSouth Dakota                 -1.105675   0.072118  -15.332  < 2e-16 ***
## StateTennessee                     0.468106   0.069431    6.742 2.08e-11 ***
## StateTexas                         0.079895   0.073768    1.083 0.278920    
## StateUtah                         -0.064121   0.070266   -0.913 0.361595    
## StateVermont                      -0.253026   0.073321   -3.451 0.000571 ***
## StateVirginia                      0.025975   0.071111    0.365 0.714947    
## StateWashington                   -0.015154   0.078407   -0.193 0.846764    
## StateWest Virginia                 0.731595   0.071295   10.261  < 2e-16 ***
## StateWisconsin                     0.055446   0.070901    0.782 0.434305    
## StateWyoming                      -0.032838   0.069908   -0.470 0.638605    
## factor(Time_Period_ID)2           -0.003472   0.062055   -0.056 0.955387    
## factor(Time_Period_ID)3            0.111961   0.062045    1.805 0.071311 .  
## factor(Time_Period_ID)4            0.163363   0.062099    2.631 0.008592 ** 
## factor(Time_Period_ID)5            0.320779   0.062165    5.160 2.73e-07 ***
## factor(Time_Period_ID)6            0.341605   0.062198    5.492 4.51e-08 ***
## factor(Time_Period_ID)7            0.484414   0.062301    7.775 1.23e-14 ***
## factor(Time_Period_ID)8            0.468420   0.062342    7.514 8.87e-14 ***
## factor(Time_Period_ID)9            0.559103   0.062466    8.951  < 2e-16 ***
## factor(Time_Period_ID)10           0.557941   0.062667    8.903  < 2e-16 ***
## factor(Time_Period_ID)11           0.678364   0.062819   10.799  < 2e-16 ***
## factor(Time_Period_ID)12           0.698451   0.063195   11.052  < 2e-16 ***
## factor(Time_Period_ID)13           0.867208   0.063499   13.657  < 2e-16 ***
## factor(Time_Period_ID)14           0.924458   0.063858   14.477  < 2e-16 ***
## factor(Time_Period_ID)15           0.975280   0.063958   15.249  < 2e-16 ***
## factor(Time_Period_ID)16           0.993784   0.064441   15.421  < 2e-16 ***
## factor(Time_Period_ID)17           1.086073   0.065089   16.686  < 2e-16 ***
## factor(Time_Period_ID)18           1.089873   0.065578   16.619  < 2e-16 ***
## factor(Time_Period_ID)19           1.079777   0.065950   16.373  < 2e-16 ***
## factor(Time_Period_ID)20           1.090787   0.066638   16.369  < 2e-16 ***
## factor(Time_Period_ID)21           1.132574   0.067332   16.821  < 2e-16 ***
## factor(Time_Period_ID)22           1.109169   0.067993   16.313  < 2e-16 ***
## factor(Time_Period_ID)23           1.257962   0.068652   18.324  < 2e-16 ***
## factor(Time_Period_ID)24           1.258759   0.069883   18.012  < 2e-16 ***
## factor(Time_Period_ID)25           1.269185   0.070409   18.026  < 2e-16 ***
## factor(Time_Period_ID)26           1.274017   0.071281   17.873  < 2e-16 ***
## factor(Time_Period_ID)27           1.376345   0.072403   19.009  < 2e-16 ***
## factor(Time_Period_ID)28           1.353182   0.073443   18.425  < 2e-16 ***
## factor(Time_Period_ID)29           1.409813   0.074810   18.845  < 2e-16 ***
## factor(Time_Period_ID)30           1.428426   0.076494   18.674  < 2e-16 ***
## factor(Time_Period_ID)31           1.532155   0.077671   19.726  < 2e-16 ***
## factor(Time_Period_ID)32           1.563880   0.080984   19.311  < 2e-16 ***
## factor(Time_Period_ID)33           1.718276   0.083272   20.634  < 2e-16 ***
## factor(Time_Period_ID)34           1.743618   0.086530   20.150  < 2e-16 ***
## factor(Time_Period_ID)35           1.797158   0.088028   20.416  < 2e-16 ***
## factor(Time_Period_ID)36           1.822423   0.090296   20.183  < 2e-16 ***
## factor(Time_Period_ID)37           1.804127   0.091132   19.797  < 2e-16 ***
## factor(Time_Period_ID)38           1.787316   0.092542   19.314  < 2e-16 ***
## factor(Time_Period_ID)39           1.831885   0.094029   19.482  < 2e-16 ***
## factor(Time_Period_ID)40           1.900976   0.094802   20.052  < 2e-16 ***
## Naloxone_Pharmacy_Yes_Redefined   -0.039833   0.046410   -0.858 0.390836    
## Naloxone_Pharmacy_No_Redefined     0.036536   0.039472    0.926 0.354756    
## Medical_Marijuana_Redefined        0.287444   0.031264    9.194  < 2e-16 ***
## Recreational_Marijuana_Redefined  -0.254885   0.047177   -5.403 7.41e-08 ***
## GSL_Redefined                      0.052181   0.032901    1.586 0.112910    
## PDMP_Redefined                    -0.165376   0.026052   -6.348 2.73e-10 ***
## Medicaid_Expansion_Redefined       0.091531   0.032270    2.836 0.004612 ** 
## pos_0_pd                          -0.011231   0.048953   -0.229 0.818565    
## pos_1_pd                          -0.048451   0.049395   -0.981 0.326778    
## pos_2_pd                          -0.012932   0.049820   -0.260 0.795219    
## pos_3_pd                          -0.050056   0.050424   -0.993 0.320991    
## pos_4_pd                          -0.053861   0.051030   -1.055 0.291339    
## pos_5_pd                          -0.093673   0.051811   -1.808 0.070773 .  
## pos_6_pd                          -0.104939   0.052810   -1.987 0.047054 *  
## pos_7_pd                          -0.104506   0.053756   -1.944 0.052036 .  
## pos_8_pd                          -0.139565   0.055417   -2.518 0.011870 *  
## pos_9_pd                          -0.149774   0.056616   -2.645 0.008227 ** 
## pos_10_pd                         -0.166228   0.057380   -2.897 0.003812 ** 
## pos_11_pd                         -0.175784   0.058660   -2.997 0.002765 ** 
## pos_12_pd                         -0.185499   0.059876   -3.098 0.001977 ** 
## pos_13_pd                         -0.248970   0.060684   -4.103 4.26e-05 ***
## pos_14_pd                         -0.236852   0.063027   -3.758 0.000177 ***
## pos_15_pd                         -0.237447   0.064595   -3.676 0.000244 ***
## pos_16_pd                         -0.245207   0.065560   -3.740 0.000189 ***
## pos_17_pd                         -0.235199   0.068093   -3.454 0.000565 ***
## pos_18_pd                         -0.201209   0.069771   -2.884 0.003973 ** 
## pos_19_pd                         -0.197819   0.070714   -2.797 0.005204 ** 
## pos_20_pd                         -0.198499   0.073765   -2.691 0.007188 ** 
## pos_21_pd                         -0.224746   0.076944   -2.921 0.003532 ** 
## pos_22_pd                         -0.237068   0.078852   -3.006 0.002678 ** 
## pos_23_pd                         -0.254062   0.080859   -3.142 0.001704 ** 
## pos_24_pd                         -0.317806   0.086316   -3.682 0.000238 ***
## pos_25_pd                         -0.288596   0.091386   -3.158 0.001614 ** 
## pos_26_pd                         -0.282744   0.092343   -3.062 0.002231 ** 
## pos_27_pd                         -0.334363   0.093438   -3.578 0.000354 ***
## pos_28_pd                         -0.313426   0.094647   -3.312 0.000946 ***
## pos_29_pd                         -0.308766   0.103231   -2.991 0.002817 ** 
## pos_30_pd                         -0.270214   0.106554   -2.536 0.011296 *  
## pos_31_pd                         -0.225267   0.110272   -2.043 0.041209 *  
## pos_32_pd                         -0.271775   0.121608   -2.235 0.025546 *  
## pos_33_pd                         -0.291040   0.127365   -2.285 0.022419 *  
## pos_34_pd                         -0.284751   0.128405   -2.218 0.026702 *  
## pos_35_pd                         -0.480443   0.149709   -3.209 0.001354 ** 
## pos_36_pd                         -0.519807   0.150596   -3.452 0.000570 ***
## pos_37_pd                         -0.488755   0.178091   -2.744 0.006120 ** 
## pos_38_pd                         -0.460498   0.240227   -1.917 0.055400 .  
## pos_39_pd                         -0.526171   0.240905   -2.184 0.029076 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.31 on 1864 degrees of freedom
## Multiple R-squared:  0.8333, Adjusted R-squared:  0.8212 
## F-statistic: 69.02 on 135 and 1864 DF,  p-value: < 2.2e-16

8.3.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_time <- model.matrix(sensitivity_anlys_post_tx_model_log_fixed_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_fixed_time <- coef(sensitivity_anlys_post_tx_model_log_fixed_time)

sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time <-
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_time), 
                                                         log(sensitivity_anlys_event_study_data$prop_dead),
                                                         coefficient_values_sensitivity_anlys_post_tx_log_fixed_time,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time
##                                        lb_coef   coef_values       ub_coef
## (Intercept)                      -10.851382923 -10.702050775 -10.552718627
## StateAlaska                       -0.129951058   0.031180346   0.192311751
## StateArizona                       0.062237502   0.200914478   0.339591454
## StateArkansas                     -0.652882056  -0.539628324  -0.426374592
## StateCalifornia                   -0.280284179  -0.142772642  -0.005261106
## StateColorado                     -0.173684644  -0.041235643   0.091213357
## StateConnecticut                   0.045712402   0.171073189   0.296433975
## StateDelaware                     -0.031299986   0.096474807   0.224249599
## StateFlorida                       0.292979359   0.400004719   0.507030079
## StateGeorgia                       0.027723313   0.125678360   0.223633407
## StateHawaii                       -0.685779652  -0.546050371  -0.406321089
## StateIdaho                        -0.300961293  -0.191457756  -0.081954219
## StateIllinois                      0.080251858   0.197690320   0.315128782
## StateIndiana                      -0.048730123   0.064617972   0.177966067
## StateIowa                         -0.740173420  -0.627597272  -0.515021123
## StateKansas                       -0.317384683  -0.221515850  -0.125647016
## StateKentucky                      0.581068006   0.667804172   0.754540338
## StateLouisiana                     0.296757848   0.391730926   0.486704004
## StateMaine                        -0.147659040   0.002398927   0.152456894
## StateMaryland                     -1.674442397  -1.476506809  -1.278571222
## StateMassachusetts                -0.345097900  -0.097092247   0.150913406
## StateMichigan                     -0.090867966   0.002757748   0.096383462
## StateMinnesota                    -0.821650971  -0.713219436  -0.604787901
## StateMississippi                  -0.216554547  -0.112657630  -0.008760714
## StateMissouri                      0.096738035   0.190079411   0.283420787
## StateMontana                      -0.588234827  -0.459116374  -0.329997922
## StateNebraska                     -1.029503669  -0.928372888  -0.827242107
## StateNevada                        0.295358200   0.433982942   0.572607685
## StateNew Hampshire                -0.026642612   0.092263156   0.211168925
## StateNew Jersey                   -0.043483622   0.103756775   0.250997172
## StateNew Mexico                    0.362396333   0.539875691   0.717355049
## StateNew York                     -0.272977371  -0.171358842  -0.069740314
## StateNorth Carolina                0.191134194   0.271801434   0.352468675
## StateNorth Dakota                 -1.360528894  -1.202644720  -1.044760545
## StateOhio                          0.438203925   0.565721688   0.693239451
## StateOklahoma                      0.315215810   0.428514846   0.541813881
## StateOregon                       -0.485201765  -0.356845277  -0.228488788
## StatePennsylvania                  0.555217503   0.653720080   0.752222658
## StateRhode Island                 -0.738417306  -0.407195727  -0.075974149
## StateSouth Carolina                0.040204678   0.134527721   0.228850765
## StateSouth Dakota                 -1.236760073  -1.105675466  -0.974590859
## StateTennessee                     0.385612730   0.468105988   0.550599245
## StateTexas                        -0.037343767   0.079895079   0.197133924
## StateUtah                         -0.210554991  -0.064121438   0.082312116
## StateVermont                      -0.390574854  -0.253025999  -0.115477145
## StateVirginia                     -0.068149296   0.025975235   0.120099766
## StateWashington                   -0.152811103  -0.015154118   0.122502867
## StateWest Virginia                 0.591308341   0.731595300   0.871882259
## StateWisconsin                    -0.036230570   0.055445595   0.147121760
## StateWyoming                      -0.149724782  -0.032837562   0.084049658
## factor(Time_Period_ID)2           -0.181519265  -0.003472000   0.174575265
## factor(Time_Period_ID)3           -0.055227592   0.111961355   0.279150301
## factor(Time_Period_ID)4           -0.006285391   0.163362774   0.333010938
## factor(Time_Period_ID)5            0.138220295   0.320779086   0.503337877
## factor(Time_Period_ID)6            0.161386982   0.341605096   0.521823210
## factor(Time_Period_ID)7            0.318677666   0.484414416   0.650151167
## factor(Time_Period_ID)8            0.295120454   0.468419545   0.641718637
## factor(Time_Period_ID)9            0.377703746   0.559103073   0.740502400
## factor(Time_Period_ID)10           0.379343358   0.557941170   0.736538981
## factor(Time_Period_ID)11           0.522387940   0.678363603   0.834339266
## factor(Time_Period_ID)12           0.534384149   0.698451222   0.862518296
## factor(Time_Period_ID)13           0.710228150   0.867207573   1.024186995
## factor(Time_Period_ID)14           0.763785558   0.924458344   1.085131130
## factor(Time_Period_ID)15           0.820705502   0.975279814   1.129854125
## factor(Time_Period_ID)16           0.836921733   0.993784049   1.150646366
## factor(Time_Period_ID)17           0.924687134   1.086073222   1.247459309
## factor(Time_Period_ID)18           0.931974678   1.089873139   1.247771600
## factor(Time_Period_ID)19           0.907643561   1.079776955   1.251910349
## factor(Time_Period_ID)20           0.928157249   1.090786661   1.253416073
## factor(Time_Period_ID)21           0.971986071   1.132573859   1.293161647
## factor(Time_Period_ID)22           0.941766455   1.109168843   1.276571231
## factor(Time_Period_ID)23           1.092144083   1.257961670   1.423779258
## factor(Time_Period_ID)24           1.087692787   1.258759316   1.429825845
## factor(Time_Period_ID)25           1.095278464   1.269185008   1.443091552
## factor(Time_Period_ID)26           1.099264213   1.274016826   1.448769438
## factor(Time_Period_ID)27           1.203118095   1.376344991   1.549571886
## factor(Time_Period_ID)28           1.179157165   1.353182162   1.527207160
## factor(Time_Period_ID)29           1.232904436   1.409812986   1.586721536
## factor(Time_Period_ID)30           1.250361393   1.428426147   1.606490902
## factor(Time_Period_ID)31           1.349878118   1.532155382   1.714432647
## factor(Time_Period_ID)32           1.378288200   1.563880462   1.749472724
## factor(Time_Period_ID)33           1.526709371   1.718276134   1.909842896
## factor(Time_Period_ID)34           1.546812535   1.743617576   1.940422617
## factor(Time_Period_ID)35           1.593457370   1.797158079   2.000858787
## factor(Time_Period_ID)36           1.619038318   1.822423180   2.025808043
## factor(Time_Period_ID)37           1.599423422   1.804126821   2.008830221
## factor(Time_Period_ID)38           1.579576918   1.787316007   1.995055097
## factor(Time_Period_ID)39           1.624105155   1.831885268   2.039665382
## factor(Time_Period_ID)40           1.692679976   1.900976476   2.109272976
## Naloxone_Pharmacy_Yes_Redefined   -0.113010705  -0.039833456   0.033343792
## Naloxone_Pharmacy_No_Redefined    -0.031499877   0.036536263   0.104572404
## Medical_Marijuana_Redefined        0.206212062   0.287444113   0.368676164
## Recreational_Marijuana_Redefined  -0.349153060  -0.254884733  -0.160616406
## GSL_Redefined                     -0.004855940   0.052181123   0.109218186
## PDMP_Redefined                    -0.224291724  -0.165376426  -0.106461127
## Medicaid_Expansion_Redefined       0.036776388   0.091530614   0.146284841
## pos_0_pd                          -0.092104177  -0.011231024   0.069642128
## pos_1_pd                          -0.141291515  -0.048450678   0.044390158
## pos_2_pd                          -0.095192514  -0.012932139   0.069328236
## pos_3_pd                          -0.132796664  -0.050055638   0.032685387
## pos_4_pd                          -0.138199101  -0.053861337   0.030476428
## pos_5_pd                          -0.180273926  -0.093673112  -0.007072299
## pos_6_pd                          -0.195746362  -0.104939487  -0.014132613
## pos_7_pd                          -0.202050379  -0.104505935  -0.006961491
## pos_8_pd                          -0.230878959  -0.139564925  -0.048250891
## pos_9_pd                          -0.250068487  -0.149774196  -0.049479905
## pos_10_pd                         -0.272512739  -0.166228035  -0.059943332
## pos_11_pd                         -0.271934547  -0.175784479  -0.079634411
## pos_12_pd                         -0.287386696  -0.185498881  -0.083611066
## pos_13_pd                         -0.369647061  -0.248970121  -0.128293180
## pos_14_pd                         -0.358517427  -0.236851871  -0.115186314
## pos_15_pd                         -0.360040382  -0.237446606  -0.114852830
## pos_16_pd                         -0.369885963  -0.245206874  -0.120527785
## pos_17_pd                         -0.370887189  -0.235198785  -0.099510382
## pos_18_pd                         -0.336745761  -0.201208698  -0.065671634
## pos_19_pd                         -0.322769400  -0.197818781  -0.072868163
## pos_20_pd                         -0.331397159  -0.198499488  -0.065601818
## pos_21_pd                         -0.366555573  -0.224745881  -0.082936190
## pos_22_pd                         -0.375518764  -0.237067702  -0.098616639
## pos_23_pd                         -0.396609992  -0.254062375  -0.111514757
## pos_24_pd                         -0.463941799  -0.317806145  -0.171670491
## pos_25_pd                         -0.452525586  -0.288595851  -0.124666115
## pos_26_pd                         -0.444015170  -0.282744218  -0.121473266
## pos_27_pd                         -0.517988369  -0.334363276  -0.150738183
## pos_28_pd                         -0.501429011  -0.313425805  -0.125422600
## pos_29_pd                         -0.515880823  -0.308765586  -0.101650350
## pos_30_pd                         -0.486482065  -0.270213547  -0.053945029
## pos_31_pd                         -0.468281637  -0.225267221   0.017747195
## pos_32_pd                         -0.514344863  -0.271775053  -0.029205243
## pos_33_pd                         -0.571399730  -0.291039751  -0.010679772
## pos_34_pd                         -0.560213029  -0.284750791  -0.009288554
## pos_35_pd                         -0.698353357  -0.480443484  -0.262533611
## pos_36_pd                         -0.727327580  -0.519806864  -0.312286149
## pos_37_pd                         -0.702127892  -0.488754579  -0.275381267
## pos_38_pd                         -0.686398257  -0.460497592  -0.234596927
## pos_39_pd                         -0.828752529  -0.526170802  -0.223589075
##                                     sd_coef
## (Intercept)                      0.07618987
## StateAlaska                      0.08220990
## StateArizona                     0.07075356
## StateArkansas                    0.05778252
## StateCalifornia                  0.07015895
## StateColorado                    0.06757602
## StateConnecticut                 0.06395958
## StateDelaware                    0.06519122
## StateFlorida                     0.05460478
## StateGeorgia                     0.04997706
## StateHawaii                      0.07129045
## StateIdaho                       0.05586915
## StateIllinois                    0.05991758
## StateIndiana                     0.05783066
## StateIowa                        0.05743681
## StateKansas                      0.04891267
## StateKentucky                    0.04425315
## StateLouisiana                   0.04845565
## StateMaine                       0.07656019
## StateMaryland                    0.10098754
## StateMassachusetts               0.12653350
## StateMichigan                    0.04776822
## StateMinnesota                   0.05532221
## StateMississippi                 0.05300863
## StateMissouri                    0.04762315
## StateMontana                     0.06587676
## StateNebraska                    0.05159734
## StateNevada                      0.07072691
## StateNew Hampshire               0.06066621
## StateNew Jersey                  0.07512265
## StateNew Mexico                  0.09055069
## StateNew York                    0.05184619
## StateNorth Carolina              0.04115676
## StateNorth Dakota                0.08055315
## StateOhio                        0.06506008
## StateOklahoma                    0.05780563
## StateOregon                      0.06548800
## StatePennsylvania                0.05025642
## StateRhode Island                0.16899060
## StateSouth Carolina              0.04812400
## StateSouth Dakota                0.06687990
## StateTennessee                   0.04208840
## StateTexas                       0.05981574
## StateUtah                        0.07471100
## StateVermont                     0.07017799
## StateVirginia                    0.04802272
## StateWashington                  0.07023316
## StateWest Virginia               0.07157498
## StateWisconsin                   0.04677355
## StateWyoming                     0.05963634
## factor(Time_Period_ID)2          0.09084044
## factor(Time_Period_ID)3          0.08530048
## factor(Time_Period_ID)4          0.08655519
## factor(Time_Period_ID)5          0.09314224
## factor(Time_Period_ID)6          0.09194802
## factor(Time_Period_ID)7          0.08455957
## factor(Time_Period_ID)8          0.08841790
## factor(Time_Period_ID)9          0.09255068
## factor(Time_Period_ID)10         0.09112133
## factor(Time_Period_ID)11         0.07957942
## factor(Time_Period_ID)12         0.08370769
## factor(Time_Period_ID)13         0.08009154
## factor(Time_Period_ID)14         0.08197591
## factor(Time_Period_ID)15         0.07886444
## factor(Time_Period_ID)16         0.08003179
## factor(Time_Period_ID)17         0.08233984
## factor(Time_Period_ID)18         0.08056044
## factor(Time_Period_ID)19         0.08782316
## factor(Time_Period_ID)20         0.08297419
## factor(Time_Period_ID)21         0.08193254
## factor(Time_Period_ID)22         0.08540938
## factor(Time_Period_ID)23         0.08460081
## factor(Time_Period_ID)24         0.08727884
## factor(Time_Period_ID)25         0.08872783
## factor(Time_Period_ID)26         0.08915950
## factor(Time_Period_ID)27         0.08838107
## factor(Time_Period_ID)28         0.08878826
## factor(Time_Period_ID)29         0.09025946
## factor(Time_Period_ID)30         0.09084936
## factor(Time_Period_ID)31         0.09299860
## factor(Time_Period_ID)32         0.09468993
## factor(Time_Period_ID)33         0.09773814
## factor(Time_Period_ID)34         0.10041074
## factor(Time_Period_ID)35         0.10392893
## factor(Time_Period_ID)36         0.10376779
## factor(Time_Period_ID)37         0.10444051
## factor(Time_Period_ID)38         0.10598933
## factor(Time_Period_ID)39         0.10601026
## factor(Time_Period_ID)40         0.10627372
## Naloxone_Pharmacy_Yes_Redefined  0.03733533
## Naloxone_Pharmacy_No_Redefined   0.03471232
## Medical_Marijuana_Redefined      0.04144492
## Recreational_Marijuana_Redefined 0.04809609
## GSL_Redefined                    0.02910054
## PDMP_Redefined                   0.03005883
## Medicaid_Expansion_Redefined     0.02793583
## pos_0_pd                         0.04126181
## pos_1_pd                         0.04736777
## pos_2_pd                         0.04196958
## pos_3_pd                         0.04221481
## pos_4_pd                         0.04302947
## pos_5_pd                         0.04418409
## pos_6_pd                         0.04633004
## pos_7_pd                         0.04976757
## pos_8_pd                         0.04658879
## pos_9_pd                         0.05117056
## pos_10_pd                        0.05422689
## pos_11_pd                        0.04905616
## pos_12_pd                        0.05198358
## pos_13_pd                        0.06156987
## pos_14_pd                        0.06207426
## pos_15_pd                        0.06254784
## pos_16_pd                        0.06361178
## pos_17_pd                        0.06922878
## pos_18_pd                        0.06915156
## pos_19_pd                        0.06375032
## pos_20_pd                        0.06780493
## pos_21_pd                        0.07235188
## pos_22_pd                        0.07063830
## pos_23_pd                        0.07272838
## pos_24_pd                        0.07455901
## pos_25_pd                        0.08363762
## pos_26_pd                        0.08228110
## pos_27_pd                        0.09368627
## pos_28_pd                        0.09592000
## pos_29_pd                        0.10567104
## pos_30_pd                        0.11034108
## pos_31_pd                        0.12398695
## pos_32_pd                        0.12376011
## pos_33_pd                        0.14304081
## pos_34_pd                        0.14054196
## pos_35_pd                        0.11117851
## pos_36_pd                        0.10587792
## pos_37_pd                        0.10886393
## pos_38_pd                        0.11525544
## pos_39_pd                        0.15437843

8.3.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_time <- sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_fixed_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_fixed_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_time$num_states <- sapply(plot_post_tx_log_fixed_time$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx_log_fixed_time, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_vline(aes(xintercept = coef(main_analysis_model_log_fixed_time)["Intervention_Redefined"]), linetype = "dashed", color = "red") +
  geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_fixed_time)["Intervention_Redefined"]), y = 12, 
            x = coef(main_analysis_model_log_fixed_time)["Intervention_Redefined"] + 0.1), color = "red")

  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

9 OLS Model Main Analysis With Linear Fixed Time Effects Interacted with Region With Log Proportion

#compute the proportion of people who died from drug overdose
main_analysis_data$prop_dead <- main_analysis_data$imputed_deaths/main_analysis_data$population


#fit an OLS with smoothed time effects
main_analysis_model_log_fixed_lin_time<-lm(log(prop_dead)~ State +
                                         Time_Period_ID:Region +
                                         I(Time_Period_ID^2):Region + 
                                         Naloxone_Pharmacy_Yes_Redefined +
                                         Naloxone_Pharmacy_No_Redefined +
                                         Medical_Marijuana_Redefined +
                                         Recreational_Marijuana_Redefined +
                                         GSL_Redefined +
                                         PDMP_Redefined +
                                         Medicaid_Expansion_Redefined +
                                         Intervention_Redefined ,
                                       data = main_analysis_data)

summary(main_analysis_model_log_fixed_lin_time)
## 
## Call:
## lm(formula = log(prop_dead) ~ State + Time_Period_ID:Region + 
##     I(Time_Period_ID^2):Region + Naloxone_Pharmacy_Yes_Redefined + 
##     Naloxone_Pharmacy_No_Redefined + Medical_Marijuana_Redefined + 
##     Recreational_Marijuana_Redefined + GSL_Redefined + PDMP_Redefined + 
##     Medicaid_Expansion_Redefined + Intervention_Redefined, data = main_analysis_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.11885 -0.14274  0.01294  0.16151  1.08925 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                         -1.077e+01  5.984e-02 -180.045  < 2e-16 ***
## StateAlaska                          3.765e-01  9.020e-02    4.174 3.13e-05 ***
## StateArizona                         5.260e-01  8.687e-02    6.055 1.69e-09 ***
## StateArkansas                       -4.947e-01  6.844e-02   -7.228 7.02e-13 ***
## StateCalifornia                      6.715e-02  9.010e-02    0.745 0.456170    
## StateColorado                        2.472e-01  9.004e-02    2.745 0.006106 ** 
## StateConnecticut                     9.452e-02  9.118e-02    1.037 0.300018    
## StateDelaware                        1.911e-01  6.967e-02    2.743 0.006149 ** 
## StateFlorida                         3.201e-01  6.849e-02    4.674 3.15e-06 ***
## StateGeorgia                         7.540e-04  6.848e-02    0.011 0.991216    
## StateHawaii                         -1.573e-01  9.011e-02   -1.746 0.080971 .  
## StateIdaho                           1.127e-01  8.783e-02    1.283 0.199685    
## StateIllinois                        1.101e-02  8.772e-02    0.126 0.900137    
## StateIndiana                        -3.875e-02  8.750e-02   -0.443 0.657902    
## StateIowa                           -7.871e-01  8.696e-02   -9.052  < 2e-16 ***
## StateKansas                         -3.434e-01  8.680e-02   -3.957 7.87e-05 ***
## StateKentucky                        6.920e-01  6.845e-02   10.109  < 2e-16 ***
## StateLouisiana                       3.491e-01  6.767e-02    5.159 2.73e-07 ***
## StateMaine                          -6.228e-02  9.377e-02   -0.664 0.506700    
## StateMaryland                       -1.509e+00  6.945e-02  -21.732  < 2e-16 ***
## StateMassachusetts                  -2.204e-01  9.110e-02   -2.420 0.015632 *  
## StateMichigan                       -1.065e-01  8.789e-02   -1.212 0.225640    
## StateMinnesota                      -7.849e-01  8.880e-02   -8.838  < 2e-16 ***
## StateMississippi                    -5.743e-02  6.772e-02   -0.848 0.396496    
## StateMissouri                        4.478e-02  8.831e-02    0.507 0.612120    
## StateMontana                        -1.949e-01  8.772e-02   -2.222 0.026399 *  
## StateNebraska                       -9.822e-01  8.789e-02  -11.175  < 2e-16 ***
## StateNevada                          6.930e-01  8.880e-02    7.804 9.72e-15 ***
## StateNew Hampshire                   1.089e-02  9.090e-02    0.120 0.904628    
## StateNew Jersey                     -5.519e-02  9.043e-02   -0.610 0.541703    
## StateNew Mexico                      8.623e-01  8.919e-02    9.668  < 2e-16 ***
## StateNew York                       -2.743e-01  9.079e-02   -3.022 0.002547 ** 
## StateNorth Carolina                  2.243e-01  6.753e-02    3.321 0.000915 ***
## StateNorth Dakota                   -1.267e+00  8.728e-02  -14.511  < 2e-16 ***
## StateOhio                            3.399e-01  8.691e-02    3.911 9.52e-05 ***
## StateOklahoma                        4.557e-01  6.816e-02    6.686 2.98e-11 ***
## StateOregon                         -6.969e-02  8.992e-02   -0.775 0.438394    
## StatePennsylvania                    4.449e-01  9.126e-02    4.875 1.18e-06 ***
## StateRhode Island                   -4.293e-01  9.162e-02   -4.686 2.98e-06 ***
## StateSouth Carolina                  2.013e-01  6.809e-02    2.957 0.003148 ** 
## StateSouth Dakota                   -1.160e+00  8.796e-02  -13.187  < 2e-16 ***
## StateTennessee                       4.640e-01  6.738e-02    6.887 7.67e-12 ***
## StateTexas                          -6.816e-03  6.842e-02   -0.100 0.920656    
## StateUtah                            1.602e-01  8.655e-02    1.851 0.064293 .  
## StateVermont                        -3.249e-01  9.116e-02   -3.564 0.000374 ***
## StateVirginia                       -2.543e-02  6.768e-02   -0.376 0.707139    
## StateWashington                      2.596e-01  9.036e-02    2.873 0.004115 ** 
## StateWest Virginia                   7.942e-01  6.850e-02   11.595  < 2e-16 ***
## StateWisconsin                      -1.123e-01  8.698e-02   -1.291 0.197017    
## StateWyoming                         2.347e-01  8.695e-02    2.699 0.007005 ** 
## Naloxone_Pharmacy_Yes_Redefined      5.414e-02  3.941e-02    1.374 0.169687    
## Naloxone_Pharmacy_No_Redefined       1.445e-02  3.883e-02    0.372 0.709784    
## Medical_Marijuana_Redefined          2.141e-01  3.118e-02    6.868 8.73e-12 ***
## Recreational_Marijuana_Redefined    -8.103e-02  4.907e-02   -1.651 0.098804 .  
## GSL_Redefined                        4.745e-02  3.175e-02    1.495 0.135166    
## PDMP_Redefined                      -1.653e-01  2.496e-02   -6.623 4.55e-11 ***
## Medicaid_Expansion_Redefined         7.859e-02  3.003e-02    2.617 0.008939 ** 
## Intervention_Redefined              -5.397e-02  2.454e-02   -2.199 0.027986 *  
## Time_Period_ID:RegionMidwest         8.179e-02  5.292e-03   15.456  < 2e-16 ***
## Time_Period_ID:RegionNortheast       7.251e-02  6.096e-03   11.896  < 2e-16 ***
## Time_Period_ID:RegionSouth           7.480e-02  4.671e-03   16.015  < 2e-16 ***
## Time_Period_ID:RegionWest            6.411e-02  5.191e-03   12.349  < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2)   -8.933e-04  1.294e-04   -6.901 6.98e-12 ***
## RegionNortheast:I(Time_Period_ID^2) -5.466e-04  1.495e-04   -3.657 0.000262 ***
## RegionSouth:I(Time_Period_ID^2)     -8.581e-04  1.189e-04   -7.217 7.61e-13 ***
## RegionWest:I(Time_Period_ID^2)      -9.039e-04  1.305e-04   -6.927 5.83e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3009 on 1934 degrees of freedom
## Multiple R-squared:  0.8371, Adjusted R-squared:  0.8316 
## F-statistic: 152.9 on 65 and 1934 DF,  p-value: < 2.2e-16
#examine fitted values
summary(fitted(main_analysis_model_log_fixed_lin_time))
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -12.209 -10.218  -9.750  -9.796  -9.329  -8.127
hist(fitted(main_analysis_model_log_fixed_lin_time))

par(mfrow = c(2,2))
plot(main_analysis_model_log_fixed_lin_time)

9.1 Coefficients and 95% CI

#compute the full dataset including basis functions
full_df_w_basis_functions_log_fixed_lin_time <- model.matrix(main_analysis_model_log_fixed_lin_time)

#estimate the 95% CI and SD
coefficient_values_log_fixed_lin_time <- coef(main_analysis_model_log_fixed_lin_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_fixed_lin_time <- compute_sd_and_CI(full_df_w_basis_functions_log_fixed_lin_time,
                                                                log(main_analysis_data$prop_dead),
                                             coefficient_values_log_fixed_lin_time,
                                             p = ncol(full_df_w_basis_functions_log_fixed_lin_time) - 50)
main_analysis_sd_and_ci_log_fixed_lin_time
##                                           lb_coef   coef_values       ub_coef
## (Intercept)                         -10.870532086 -1.077330e+01 -1.067607e+01
## StateAlaska                           0.227816678  3.764610e-01  5.251054e-01
## StateArizona                          0.390612117  5.259709e-01  6.613297e-01
## StateArkansas                        -0.604794078 -4.946764e-01 -3.845586e-01
## StateCalifornia                      -0.089434784  6.715414e-02  2.237431e-01
## StateColorado                         0.108661454  2.471601e-01  3.856588e-01
## StateConnecticut                     -0.144557560  9.452006e-02  3.335977e-01
## StateDelaware                         0.067867770  1.910826e-01  3.142975e-01
## StateFlorida                          0.213681393  3.201422e-01  4.266031e-01
## StateGeorgia                         -0.086244949  7.539808e-04  8.775291e-02
## StateHawaii                          -0.302406580 -1.573225e-01 -1.223844e-02
## StateIdaho                           -0.028208915  1.126758e-01  2.535605e-01
## StateIllinois                        -0.161293636  1.100985e-02  1.833133e-01
## StateIndiana                         -0.190069700 -3.875005e-02  1.125696e-01
## StateIowa                            -0.922491125 -7.871038e-01 -6.517165e-01
## StateKansas                          -0.476952541 -3.434288e-01 -2.099050e-01
## StateKentucky                         0.605308589  6.919793e-01  7.786499e-01
## StateLouisiana                        0.250558266  3.491381e-01  4.477179e-01
## StateMaine                           -0.307386749 -6.227663e-02  1.828335e-01
## StateMaryland                        -1.708316110 -1.509208e+00 -1.310100e+00
## StateMassachusetts                   -0.561705395 -2.204241e-01  1.208572e-01
## StateMichigan                        -0.239268393 -1.065315e-01  2.620537e-02
## StateMinnesota                       -0.923565633 -7.848809e-01 -6.461961e-01
## StateMississippi                     -0.152855044 -5.743181e-02  3.799143e-02
## StateMissouri                        -0.085733292  4.478408e-02  1.753014e-01
## StateMontana                         -0.336215945 -1.949090e-01 -5.360210e-02
## StateNebraska                        -1.113111783 -9.821615e-01 -8.512112e-01
## StateNevada                           0.547851351  6.929982e-01  8.381450e-01
## StateNew Hampshire                   -0.220119819  1.089307e-02  2.419060e-01
## StateNew Jersey                      -0.309227369 -5.519172e-02  1.988439e-01
## StateNew Mexico                       0.703870882  8.622936e-01  1.020716e+00
## StateNew York                        -0.505083199 -2.743314e-01 -4.357956e-02
## StateNorth Carolina                   0.136280670  2.242541e-01  3.122274e-01
## StateNorth Dakota                    -1.442024087 -1.266542e+00 -1.091059e+00
## StateOhio                             0.204411181  3.398957e-01  4.753802e-01
## StateOklahoma                         0.345493483  4.557456e-01  5.659976e-01
## StateOregon                          -0.209913729 -6.969390e-02  7.052594e-02
## StatePennsylvania                     0.222212940  4.448805e-01  6.675480e-01
## StateRhode Island                    -0.837302163 -4.292993e-01 -2.129647e-02
## StateSouth Carolina                   0.111509198  2.013118e-01  2.911145e-01
## StateSouth Dakota                    -1.317921300 -1.159922e+00 -1.001924e+00
## StateTennessee                        0.379504435  4.640316e-01  5.485588e-01
## StateTexas                           -0.121362607 -6.816327e-03  1.077300e-01
## StateUtah                            -0.043845600  1.602299e-01  3.643053e-01
## StateVermont                         -0.572803061 -3.249195e-01 -7.703584e-02
## StateVirginia                        -0.122942397 -2.542955e-02  7.208329e-02
## StateWashington                       0.117677605  2.595663e-01  4.014550e-01
## StateWest Virginia                    0.652987520  7.942308e-01  9.354740e-01
## StateWisconsin                       -0.237211780 -1.122536e-01  1.270455e-02
## StateWyoming                          0.067986094  2.347091e-01  4.014321e-01
## Naloxone_Pharmacy_Yes_Redefined      -0.009128978  5.413660e-02  1.174022e-01
## Naloxone_Pharmacy_No_Redefined       -0.047020174  1.445200e-02  7.592417e-02
## Medical_Marijuana_Redefined           0.145383479  2.141197e-01  2.828558e-01
## Recreational_Marijuana_Redefined     -0.155713354 -8.103395e-02 -6.354555e-03
## GSL_Redefined                        -0.005849108  4.745038e-02  1.007499e-01
## PDMP_Redefined                       -0.218050934 -1.652800e-01 -1.125091e-01
## Medicaid_Expansion_Redefined          0.028563796  7.859406e-02  1.286243e-01
## Intervention_Redefined               -0.099588037 -5.397472e-02 -8.361396e-03
## Time_Period_ID:RegionMidwest          0.072485767  8.178652e-02  9.108728e-02
## Time_Period_ID:RegionNortheast        0.050914470  7.251276e-02  9.411106e-02
## Time_Period_ID:RegionSouth            0.066136530  7.480447e-02  8.347241e-02
## Time_Period_ID:RegionWest             0.054947367  6.410565e-02  7.326393e-02
## RegionMidwest:I(Time_Period_ID^2)    -0.001107586 -8.933230e-04 -6.790600e-04
## RegionNortheast:I(Time_Period_ID^2)  -0.001003649 -5.465679e-04 -8.948637e-05
## RegionSouth:I(Time_Period_ID^2)      -0.001078072 -8.581239e-04 -6.381757e-04
## RegionWest:I(Time_Period_ID^2)       -0.001120720 -9.038570e-04 -6.869936e-04
##                                          sd_coef
## (Intercept)                         0.0496071198
## StateAlaska                         0.0758389536
## StateArizona                        0.0690606190
## StateArkansas                       0.0561825087
## StateCalifornia                     0.0798923104
## StateColorado                       0.0706625829
## StateConnecticut                    0.1219783755
## StateDelaware                       0.0628647209
## StateFlorida                        0.0543167495
## StateGeorgia                        0.0443872093
## StateHawaii                         0.0740224857
## StateIdaho                          0.0718799472
## StateIllinois                       0.0879099441
## StateIndiana                        0.0772039012
## StateIowa                           0.0690751589
## StateKansas                         0.0681243626
## StateKentucky                       0.0442197305
## StateLouisiana                      0.0502958363
## StateMaine                          0.1250561821
## StateMaryland                       0.1015857987
## StateMassachusetts                  0.1741231035
## StateMichigan                       0.0677228979
## StateMinnesota                      0.0707575372
## StateMississippi                    0.0486853239
## StateMissouri                       0.0665904937
## StateMontana                        0.0720953687
## StateNebraska                       0.0668113767
## StateNevada                         0.0740545048
## StateNew Hampshire                  0.1178637172
## StateNew Jersey                     0.1296100240
## StateNew Mexico                     0.0808279105
## StateNew York                       0.1177305210
## StateNorth Carolina                 0.0448843790
## StateNorth Dakota                   0.0895317936
## StateOhio                           0.0691247462
## StateOklahoma                       0.0562510604
## StateOregon                         0.0715407308
## StatePennsylvania                   0.1136058778
## StateRhode Island                   0.2081647169
## StateSouth Carolina                 0.0458176666
## StateSouth Dakota                   0.0806116835
## StateTennessee                      0.0431261187
## StateTexas                          0.0584419796
## StateUtah                           0.1041201296
## StateVermont                        0.1264712293
## StateVirginia                       0.0497514504
## StateWashington                     0.0723921994
## StateWest Virginia                  0.0720628801
## StateWisconsin                      0.0637541664
## StateWyoming                        0.0850627595
## Naloxone_Pharmacy_Yes_Redefined     0.0322783540
## Naloxone_Pharmacy_No_Redefined      0.0313633541
## Medical_Marijuana_Redefined         0.0350694817
## Recreational_Marijuana_Redefined    0.0381017345
## GSL_Redefined                       0.0271936176
## PDMP_Redefined                      0.0269239364
## Medicaid_Expansion_Redefined        0.0255256427
## Intervention_Redefined              0.0232721023
## Time_Period_ID:RegionMidwest        0.0047452848
## Time_Period_ID:RegionNortheast      0.0110195384
## Time_Period_ID:RegionSouth          0.0044224191
## Time_Period_ID:RegionWest           0.0046725918
## RegionMidwest:I(Time_Period_ID^2)   0.0001093179
## RegionNortheast:I(Time_Period_ID^2) 0.0002332049
## RegionSouth:I(Time_Period_ID^2)     0.0001122185
## RegionWest:I(Time_Period_ID^2)      0.0001106446

9.1.1 Attributable Deaths

date_data <- main_analysis_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_lin_time <- attr_death_compute(main_analysis_data,
                                                   main_analysis_sd_and_ci_log_fixed_lin_time, 
                                                   post_tx_model = FALSE, tx_name = "Intervention_Redefined")
attr_deaths_est_log_lin_time <- merge(attr_deaths_est_log_lin_time, date_data, 
                                                    by.x = "Time_Period", by.y = "Time_Period_ID")

ggplot(attr_deaths_est_log_lin_time, aes(x = Time_Period_Start)) + 
  # geom_point(aes(y = attr_deaths)) + 
  geom_line(aes(y = attr_deaths, linetype = "Estimate")) + 
  # geom_point(aes(y = attr_deaths_lb)) + 
  geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) + 
  # geom_point(aes(y = attr_deaths_ub)) + 
  geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) + 
  labs(x = "Date", y = "Attributable Deaths",
       title = "Estimated Number of Attributable Deaths Using Linear and Quad. Time Effects, 
       Log Probability of Drug Overdose Death",
       linetype = "") + 
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black")) + 
  scale_linetype_manual(values = c("dashed", "solid"))

9.2 Linear Policy Measures

#use this function to compute the cumulative sum, but resets the sum if the variable was 0
compute_cumsum = function(x){
    cs = cumsum(x)
    cs - cummax((x == 0) * cs)
}
sensitivity_anlys_event_study_data_lin_post_tx <- sensitivity_anlys_event_study_data %>%
  arrange(State, Time_Period_ID) %>%
  group_by(State) %>%
  mutate(sum_tx_periods = pos_0_pd + pos_1_pd + pos_2_pd + pos_3_pd + 
           pos_4_pd + pos_5_pd + pos_6_pd + pos_7_pd + pos_8_pd + pos_9_pd + 
           pos_10_pd + pos_11_pd + pos_12_pd + pos_13_pd + pos_14_pd + 
           pos_15_pd + pos_16_pd + pos_17_pd + pos_18_pd + pos_19_pd + 
           pos_20_pd + pos_21_pd + pos_22_pd + pos_23_pd + pos_24_pd + 
           pos_25_pd + pos_26_pd + pos_27_pd + pos_28_pd + pos_29_pd + 
           pos_30_pd + pos_31_pd + pos_32_pd + pos_33_pd + pos_34_pd + 
           pos_35_pd + pos_36_pd + pos_37_pd + pos_38_pd + pos_39_pd,
         time_after_tx = compute_cumsum(sum_tx_periods),
         num_pd_w_tx = compute_cumsum(Intervention_Redefined),
         num_pd_w_naloxone_yes = compute_cumsum(Naloxone_Pharmacy_Yes_Redefined),
         num_pd_w_naloxone_no = compute_cumsum(Naloxone_Pharmacy_No_Redefined),
         num_pd_w_med_marijuana = compute_cumsum(Medical_Marijuana_Redefined),
         num_pd_w_rec_marijuana = compute_cumsum(Recreational_Marijuana_Redefined),
         num_pd_w_gsl = compute_cumsum(GSL_Redefined),
         num_pd_w_pdmp = compute_cumsum(PDMP_Redefined),
         num_pd_w_medicaid = compute_cumsum(Medicaid_Expansion_Redefined),
         lag_num_pd_w_tx = lag(num_pd_w_tx))

sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx[is.na(sensitivity_anlys_event_study_data_lin_post_tx$lag_num_pd_w_tx)] <- 0
  
#run the gam model
sensitivity_anlys_lin_post_tx_model_linear_time<-lm(log(prop_dead)~ State +
                                                      Time_Period_ID:Region  +
                                                      I(Time_Period_ID^2):Region + 
                                                      num_pd_w_naloxone_yes +
                                                      num_pd_w_naloxone_no +
                                                      num_pd_w_med_marijuana +
                                                      num_pd_w_rec_marijuana +
                                                      num_pd_w_gsl +
                                                      num_pd_w_pdmp +
                                                      num_pd_w_medicaid +
                                                      Intervention_Redefined+
                                                      lag_num_pd_w_tx,
                                                    data = sensitivity_anlys_event_study_data_lin_post_tx)
summary(sensitivity_anlys_lin_post_tx_model_linear_time)
## 
## Call:
## lm(formula = log(prop_dead) ~ State + Time_Period_ID:Region + 
##     I(Time_Period_ID^2):Region + num_pd_w_naloxone_yes + num_pd_w_naloxone_no + 
##     num_pd_w_med_marijuana + num_pd_w_rec_marijuana + num_pd_w_gsl + 
##     num_pd_w_pdmp + num_pd_w_medicaid + Intervention_Redefined + 
##     lag_num_pd_w_tx, data = sensitivity_anlys_event_study_data_lin_post_tx)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.22313 -0.13603  0.01109  0.15412  1.09172 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                         -1.081e+01  5.983e-02 -180.708  < 2e-16 ***
## StateAlaska                          5.265e-01  8.961e-02    5.876 4.95e-09 ***
## StateArizona                         4.732e-01  9.036e-02    5.237 1.81e-07 ***
## StateArkansas                       -4.311e-01  6.966e-02   -6.189 7.38e-10 ***
## StateCalifornia                      3.097e-01  9.223e-02    3.358 0.000800 ***
## StateColorado                        4.190e-01  8.859e-02    4.729 2.42e-06 ***
## StateConnecticut                     3.481e-02  9.355e-02    0.372 0.709872    
## StateDelaware                        2.790e-01  7.059e-02    3.952 8.04e-05 ***
## StateFlorida                         5.838e-01  7.199e-02    8.110 8.91e-16 ***
## StateGeorgia                         3.100e-01  7.384e-02    4.199 2.80e-05 ***
## StateHawaii                         -1.777e-01  9.066e-02   -1.960 0.050118 .  
## StateIdaho                          -2.427e-01  9.291e-02   -2.612 0.009070 ** 
## StateIllinois                        2.272e-02  9.231e-02    0.246 0.805600    
## StateIndiana                        -2.942e-01  9.057e-02   -3.249 0.001179 ** 
## StateIowa                           -7.920e-01  8.697e-02   -9.107  < 2e-16 ***
## StateKansas                         -3.569e-01  8.635e-02   -4.133 3.74e-05 ***
## StateKentucky                        5.010e-01  7.098e-02    7.059 2.34e-12 ***
## StateLouisiana                       4.570e-01  6.807e-02    6.714 2.49e-11 ***
## StateMaine                           1.134e-01  9.586e-02    1.183 0.237057    
## StateMaryland                       -1.259e+00  7.266e-02  -17.334  < 2e-16 ***
## StateMassachusetts                  -4.600e-01  9.202e-02   -4.998 6.31e-07 ***
## StateMichigan                       -9.613e-02  9.093e-02   -1.057 0.290537    
## StateMinnesota                      -6.145e-01  8.934e-02   -6.879 8.11e-12 ***
## StateMississippi                    -1.524e-01  6.811e-02   -2.237 0.025377 *  
## StateMissouri                        2.503e-01  8.865e-02    2.824 0.004795 ** 
## StateMontana                         1.278e-01  9.014e-02    1.418 0.156450    
## StateNebraska                       -1.018e+00  8.815e-02  -11.544  < 2e-16 ***
## StateNevada                          8.067e-01  8.896e-02    9.067  < 2e-16 ***
## StateNew Hampshire                  -1.251e-02  9.376e-02   -0.133 0.893884    
## StateNew Jersey                      1.547e-02  9.339e-02    0.166 0.868419    
## StateNew Mexico                      8.940e-01  9.177e-02    9.741  < 2e-16 ***
## StateNew York                       -4.983e-01  9.161e-02   -5.439 6.04e-08 ***
## StateNorth Carolina                  2.940e-01  6.775e-02    4.339 1.50e-05 ***
## StateNorth Dakota                   -1.392e+00  8.757e-02  -15.891  < 2e-16 ***
## StateOhio                            4.864e-01  8.964e-02    5.426 6.48e-08 ***
## StateOklahoma                        3.140e-01  7.060e-02    4.448 9.16e-06 ***
## StateOregon                          2.450e-01  8.915e-02    2.748 0.006048 ** 
## StatePennsylvania                    3.417e-01  9.446e-02    3.617 0.000305 ***
## StateRhode Island                   -5.881e-01  9.285e-02   -6.334 2.96e-10 ***
## StateSouth Carolina                  1.258e-01  6.874e-02    1.830 0.067393 .  
## StateSouth Dakota                   -1.251e+00  8.884e-02  -14.080  < 2e-16 ***
## StateTennessee                       4.218e-01  6.737e-02    6.261 4.69e-10 ***
## StateTexas                           3.528e-02  7.309e-02    0.483 0.629342    
## StateUtah                           -4.513e-02  9.206e-02   -0.490 0.624001    
## StateVermont                        -2.578e-01  9.103e-02   -2.832 0.004671 ** 
## StateVirginia                        1.442e-02  6.906e-02    0.209 0.834616    
## StateWashington                      4.951e-01  8.928e-02    5.546 3.33e-08 ***
## StateWest Virginia                   6.012e-01  7.160e-02    8.397  < 2e-16 ***
## StateWisconsin                      -2.082e-02  8.706e-02   -0.239 0.811027    
## StateWyoming                         1.606e-02  9.063e-02    0.177 0.859364    
## num_pd_w_naloxone_yes               -7.162e-03  5.598e-03   -1.279 0.200931    
## num_pd_w_naloxone_no                -1.361e-02  3.652e-03   -3.727 0.000200 ***
## num_pd_w_med_marijuana              -9.307e-03  2.199e-03   -4.233 2.41e-05 ***
## num_pd_w_rec_marijuana              -2.385e-02  8.065e-03   -2.957 0.003144 ** 
## num_pd_w_gsl                         1.578e-02  3.819e-03    4.133 3.74e-05 ***
## num_pd_w_pdmp                        8.359e-03  2.272e-03    3.679 0.000240 ***
## num_pd_w_medicaid                    2.492e-02  4.310e-03    5.781 8.64e-09 ***
## Intervention_Redefined              -7.822e-02  2.481e-02   -3.153 0.001643 ** 
## lag_num_pd_w_tx                     -1.528e-02  1.851e-03   -8.255 2.77e-16 ***
## Time_Period_ID:RegionMidwest         7.835e-02  5.207e-03   15.049  < 2e-16 ***
## Time_Period_ID:RegionNortheast       7.695e-02  6.247e-03   12.317  < 2e-16 ***
## Time_Period_ID:RegionSouth           6.482e-02  4.704e-03   13.779  < 2e-16 ***
## Time_Period_ID:RegionWest            6.953e-02  5.575e-03   12.472  < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2)   -7.113e-04  1.317e-04   -5.401 7.46e-08 ***
## RegionNortheast:I(Time_Period_ID^2) -4.616e-04  1.578e-04   -2.925 0.003483 ** 
## RegionSouth:I(Time_Period_ID^2)     -5.745e-04  1.242e-04   -4.626 3.97e-06 ***
## RegionWest:I(Time_Period_ID^2)      -9.302e-04  1.360e-04   -6.842 1.05e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2987 on 1933 degrees of freedom
## Multiple R-squared:  0.8395, Adjusted R-squared:  0.8341 
## F-statistic: 153.2 on 66 and 1933 DF,  p-value: < 2.2e-16

9.2.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_log_fixed_lin_time_lin_post_tx <- model.matrix(sensitivity_anlys_lin_post_tx_model_linear_time)

#estimate the 95% CI and SD
coefficient_values_log_fixed_lin_time_lin_post_tx <- coef(sensitivity_anlys_lin_post_tx_model_linear_time)
#type = "response" to get the estimated probabilities
main_analysis_sd_and_ci_log_fixed_lin_time_lin_post_tx <- compute_sd_and_CI(full_df_w_basis_functions_log_fixed_lin_time_lin_post_tx,
                                                                log(sensitivity_anlys_event_study_data_lin_post_tx$prop_dead),
                                             coefficient_values_log_fixed_lin_time_lin_post_tx,
                                             p = ncol(full_df_w_basis_functions_log_fixed_lin_time_lin_post_tx) - 50)
round(main_analysis_sd_and_ci_log_fixed_lin_time_lin_post_tx,4)
##                                      lb_coef coef_values  ub_coef sd_coef
## (Intercept)                         -10.8971    -10.8119 -10.7267  0.0435
## StateAlaska                           0.3782      0.5265   0.6749  0.0757
## StateArizona                          0.3236      0.4732   0.6229  0.0764
## StateArkansas                        -0.5372     -0.4311  -0.3250  0.0541
## StateCalifornia                       0.1508      0.3097   0.4686  0.0811
## StateColorado                         0.2997      0.4190   0.5382  0.0609
## StateConnecticut                     -0.2137      0.0348   0.2833  0.1268
## StateDelaware                         0.1722      0.2790   0.3857  0.0544
## StateFlorida                          0.4703      0.5838   0.6974  0.0580
## StateGeorgia                          0.2049      0.3100   0.4152  0.0537
## StateHawaii                          -0.3154     -0.1777  -0.0400  0.0703
## StateIdaho                           -0.4075     -0.2427  -0.0779  0.0841
## StateIllinois                        -0.1358      0.0227   0.1813  0.0809
## StateIndiana                         -0.4417     -0.2942  -0.1467  0.0753
## StateIowa                            -0.9155     -0.7920  -0.6684  0.0630
## StateKansas                          -0.4841     -0.3569  -0.2297  0.0649
## StateKentucky                         0.4072      0.5010   0.5949  0.0479
## StateLouisiana                        0.3600      0.4570   0.5539  0.0495
## StateMaine                           -0.1363      0.1134   0.3630  0.1274
## StateMaryland                        -1.4542     -1.2595  -1.0647  0.0994
## StateMassachusetts                   -0.8118     -0.4600  -0.1081  0.1795
## StateMichigan                        -0.2281     -0.0961   0.0358  0.0673
## StateMinnesota                       -0.7400     -0.6145  -0.4891  0.0640
## StateMississippi                     -0.2577     -0.1524  -0.0471  0.0537
## StateMissouri                         0.1236      0.2503   0.3771  0.0647
## StateMontana                         -0.0338      0.1278   0.2893  0.0824
## StateNebraska                        -1.1396     -1.0176  -0.8955  0.0623
## StateNevada                           0.6796      0.8067   0.9337  0.0648
## StateNew Hampshire                   -0.2309     -0.0125   0.2059  0.1114
## StateNew Jersey                      -0.2259      0.0155   0.2569  0.1232
## StateNew Mexico                       0.7175      0.8940   1.0705  0.0901
## StateNew York                        -0.7476     -0.4983  -0.2490  0.1272
## StateNorth Carolina                   0.2159      0.2940   0.3720  0.0398
## StateNorth Dakota                    -1.5705     -1.3916  -1.2127  0.0913
## StateOhio                             0.3467      0.4864   0.6261  0.0713
## StateOklahoma                         0.2124      0.3140   0.4157  0.0519
## StateOregon                           0.1198      0.2450   0.3702  0.0639
## StatePennsylvania                     0.1129      0.3417   0.5705  0.1167
## StateRhode Island                    -1.0350     -0.5881  -0.1413  0.2280
## StateSouth Carolina                   0.0338      0.1258   0.2178  0.0469
## StateSouth Dakota                    -1.4037     -1.2508  -1.0979  0.0780
## StateTennessee                        0.3499      0.4218   0.4938  0.0367
## StateTexas                           -0.0672      0.0353   0.1378  0.0523
## StateUtah                            -0.2766     -0.0451   0.1863  0.1181
## StateVermont                         -0.4935     -0.2578  -0.0222  0.1202
## StateVirginia                        -0.0759      0.0144   0.1048  0.0461
## StateWashington                       0.3654      0.4951   0.6248  0.0662
## StateWest Virginia                    0.4548      0.6012   0.7476  0.0747
## StateWisconsin                       -0.1383     -0.0208   0.0966  0.0599
## StateWyoming                         -0.1504      0.0161   0.1825  0.0849
## num_pd_w_naloxone_yes                -0.0174     -0.0072   0.0031  0.0052
## num_pd_w_naloxone_no                 -0.0200     -0.0136  -0.0073  0.0032
## num_pd_w_med_marijuana               -0.0144     -0.0093  -0.0042  0.0026
## num_pd_w_rec_marijuana               -0.0360     -0.0238  -0.0117  0.0062
## num_pd_w_gsl                          0.0073      0.0158   0.0243  0.0043
## num_pd_w_pdmp                         0.0035      0.0084   0.0132  0.0025
## num_pd_w_medicaid                     0.0172      0.0249   0.0326  0.0039
## Intervention_Redefined               -0.1254     -0.0782  -0.0310  0.0241
## lag_num_pd_w_tx                      -0.0193     -0.0153  -0.0113  0.0020
## Time_Period_ID:RegionMidwest          0.0694      0.0784   0.0873  0.0045
## Time_Period_ID:RegionNortheast        0.0556      0.0769   0.0983  0.0109
## Time_Period_ID:RegionSouth            0.0572      0.0648   0.0724  0.0039
## Time_Period_ID:RegionWest             0.0587      0.0695   0.0804  0.0055
## RegionMidwest:I(Time_Period_ID^2)    -0.0009     -0.0007  -0.0005  0.0001
## RegionNortheast:I(Time_Period_ID^2)  -0.0009     -0.0005   0.0000  0.0002
## RegionSouth:I(Time_Period_ID^2)      -0.0008     -0.0006  -0.0004  0.0001
## RegionWest:I(Time_Period_ID^2)       -0.0012     -0.0009  -0.0007  0.0001

9.2.2 Attributable Deaths

date_data <- main_analysis_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_lin_time_lin_post_tx <- attr_death_compute(sensitivity_anlys_event_study_data_lin_post_tx,
                                                   main_analysis_sd_and_ci_log_fixed_lin_time_lin_post_tx, 
                                                   post_tx_model = FALSE, tx_name = "num_pd_w_tx")
attr_deaths_est_log_lin_time_lin_post_tx <- merge(attr_deaths_est_log_lin_time_lin_post_tx, date_data, 
                                                    by.x = "Time_Period", by.y = "Time_Period_ID")

ggplot(attr_deaths_est_log_lin_time_lin_post_tx, aes(x = Time_Period_Start)) + 
  # geom_point(aes(y = attr_deaths)) + 
  geom_line(aes(y = attr_deaths, linetype = "Estimate")) + 
  # geom_point(aes(y = attr_deaths_lb)) + 
  geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) + 
  # geom_point(aes(y = attr_deaths_ub)) + 
  geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) + 
  labs(x = "Date", y = "Attributable Deaths",
       title = "Estimated Number of Attributable Deaths Using Linear and Quad. Time Effects, 
       Log Probability of Drug Overdose Death, Linear Policy Effects",
       linetype = "") + 
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black")) + 
  scale_linetype_manual(values = c("dashed", "solid"))

9.3 Event Study

9.3.1 Model Fitting

#create a formula for the gam model which includes the state effects, smoothed time effects, policy measures, 
#the periods before the intervention (excluding 1 period and 34 periods before intervention)
#the intervention period, and the periods after the intervention

formula_event_study_log_fixed_lin_time <- formula(paste("log(prop_dead) ~ State +
                                           Time_Period_ID:Region  +
                                           I(Time_Period_ID^2):Region + 
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)-2), 
                                            function(x)paste("neg_", x, "_pd", sep = "")), collapse = "+"),
                                     "+",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_event_study_model_log_fixed_lin_time<-lm(formula_event_study_log_fixed_lin_time,
                                         data = sensitivity_anlys_event_study_data)

summary(sensitivity_anlys_event_study_model_log_fixed_lin_time)
## 
## Call:
## lm(formula = formula_event_study_log_fixed_lin_time, data = sensitivity_anlys_event_study_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.94531 -0.13453  0.01384  0.15668  1.02461 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                         -1.075e+01  9.544e-02 -112.655  < 2e-16 ***
## StateAlaska                          3.681e-01  1.075e-01    3.426 0.000626 ***
## StateArizona                         5.417e-01  9.088e-02    5.961 2.99e-09 ***
## StateArkansas                       -5.239e-01  7.259e-02   -7.216 7.74e-13 ***
## StateCalifornia                      2.073e-01  1.047e-01    1.979 0.047963 *  
## StateColorado                        2.631e-01  9.303e-02    2.828 0.004731 ** 
## StateConnecticut                     9.640e-02  9.110e-02    1.058 0.290105    
## StateDelaware                        1.371e-01  9.579e-02    1.431 0.152515    
## StateFlorida                         4.217e-01  8.768e-02    4.810 1.63e-06 ***
## StateGeorgia                         1.256e-01  9.359e-02    1.342 0.179679    
## StateHawaii                         -1.940e-01  9.856e-02   -1.968 0.049189 *  
## StateIdaho                           1.268e-01  1.020e-01    1.244 0.213751    
## StateIllinois                        6.142e-02  9.772e-02    0.629 0.529744    
## StateIndiana                        -7.033e-02  8.764e-02   -0.802 0.422390    
## StateIowa                           -7.574e-01  9.173e-02   -8.257 2.80e-16 ***
## StateKansas                         -3.589e-01  8.637e-02   -4.155 3.40e-05 ***
## StateKentucky                        6.751e-01  7.308e-02    9.238  < 2e-16 ***
## StateLouisiana                       4.021e-01  7.420e-02    5.419 6.78e-08 ***
## StateMaine                          -6.443e-02  9.467e-02   -0.681 0.496190    
## StateMaryland                       -1.450e+00  8.167e-02  -17.755  < 2e-16 ***
## StateMassachusetts                  -2.100e-01  9.102e-02   -2.307 0.021172 *  
## StateMichigan                       -8.755e-02  8.965e-02   -0.977 0.328865    
## StateMinnesota                      -8.065e-01  8.839e-02   -9.124  < 2e-16 ***
## StateMississippi                    -9.381e-02  8.422e-02   -1.114 0.265434    
## StateMissouri                        4.407e-02  9.107e-02    0.484 0.628464    
## StateMontana                        -1.026e-01  9.498e-02   -1.080 0.280276    
## StateNebraska                       -1.044e+00  9.408e-02  -11.101  < 2e-16 ***
## StateNevada                          7.785e-01  9.129e-02    8.527  < 2e-16 ***
## StateNew Hampshire                  -2.938e-03  9.185e-02   -0.032 0.974486    
## StateNew Jersey                      1.872e-02  1.003e-01    0.187 0.851990    
## StateNew Mexico                      8.850e-01  8.919e-02    9.923  < 2e-16 ***
## StateNew York                       -2.568e-01  9.076e-02   -2.830 0.004707 ** 
## StateNorth Carolina                  2.672e-01  7.077e-02    3.776 0.000164 ***
## StateNorth Dakota                   -1.325e+00  9.366e-02  -14.146  < 2e-16 ***
## StateOhio                            4.498e-01  1.090e-01    4.128 3.83e-05 ***
## StateOklahoma                        4.440e-01  7.182e-02    6.181 7.79e-10 ***
## StateOregon                         -4.697e-02  8.988e-02   -0.523 0.601342    
## StatePennsylvania                    5.675e-01  1.067e-01    5.316 1.19e-07 ***
## StateRhode Island                   -4.515e-01  1.034e-01   -4.368 1.32e-05 ***
## StateSouth Carolina                  1.590e-01  9.194e-02    1.730 0.083853 .  
## StateSouth Dakota                   -1.233e+00  1.078e-01  -11.438  < 2e-16 ***
## StateTennessee                       4.662e-01  6.651e-02    7.009 3.34e-12 ***
## StateTexas                           9.686e-02  8.446e-02    1.147 0.251623    
## StateUtah                            2.479e-01  8.977e-02    2.761 0.005817 ** 
## StateVermont                        -3.360e-01  9.209e-02   -3.648 0.000271 ***
## StateVirginia                        3.640e-02  7.555e-02    0.482 0.629990    
## StateWashington                      2.882e-01  8.980e-02    3.210 0.001351 ** 
## StateWest Virginia                   7.654e-01  7.839e-02    9.763  < 2e-16 ***
## StateWisconsin                      -8.544e-02  9.307e-02   -0.918 0.358705    
## StateWyoming                         2.723e-01  8.661e-02    3.144 0.001695 ** 
## Naloxone_Pharmacy_Yes_Redefined      5.742e-02  3.942e-02    1.457 0.145393    
## Naloxone_Pharmacy_No_Redefined       1.750e-02  3.877e-02    0.452 0.651676    
## Medical_Marijuana_Redefined          2.179e-01  3.148e-02    6.922 6.11e-12 ***
## Recreational_Marijuana_Redefined    -7.658e-02  4.945e-02   -1.549 0.121609    
## GSL_Redefined                        5.952e-02  3.170e-02    1.877 0.060623 .  
## PDMP_Redefined                      -1.878e-01  2.513e-02   -7.472 1.20e-13 ***
## Medicaid_Expansion_Redefined         7.906e-02  3.021e-02    2.617 0.008940 ** 
## neg_2_pd                             2.811e-02  6.097e-02    0.461 0.644868    
## neg_3_pd                             3.165e-02  6.190e-02    0.511 0.609135    
## neg_4_pd                             7.850e-03  6.316e-02    0.124 0.901104    
## neg_5_pd                             3.932e-03  6.385e-02    0.062 0.950903    
## neg_6_pd                             7.330e-03  6.594e-02    0.111 0.911513    
## neg_7_pd                            -4.042e-02  6.705e-02   -0.603 0.546673    
## neg_8_pd                            -1.028e-01  6.875e-02   -1.496 0.134855    
## neg_9_pd                            -3.113e-02  7.163e-02   -0.435 0.663913    
## neg_10_pd                            1.448e-02  7.375e-02    0.196 0.844339    
## neg_11_pd                            1.979e-02  7.618e-02    0.260 0.795086    
## neg_12_pd                            1.120e-01  8.058e-02    1.390 0.164807    
## neg_13_pd                            1.633e-02  8.271e-02    0.197 0.843482    
## neg_14_pd                           -1.026e-02  8.494e-02   -0.121 0.903825    
## neg_15_pd                           -5.217e-02  8.733e-02   -0.597 0.550303    
## neg_16_pd                           -3.652e-02  9.162e-02   -0.399 0.690262    
## neg_17_pd                           -4.312e-02  9.690e-02   -0.445 0.656356    
## neg_18_pd                           -3.964e-02  1.003e-01   -0.395 0.692646    
## neg_19_pd                           -1.457e-01  1.036e-01   -1.407 0.159592    
## neg_20_pd                           -1.913e-01  1.096e-01   -1.745 0.081105 .  
## neg_21_pd                           -1.223e-01  1.168e-01   -1.048 0.294990    
## neg_22_pd                           -1.057e-01  1.195e-01   -0.885 0.376474    
## neg_23_pd                           -1.248e-01  1.238e-01   -1.008 0.313537    
## neg_24_pd                           -1.803e-01  1.330e-01   -1.355 0.175496    
## neg_25_pd                           -4.070e-02  1.356e-01   -0.300 0.764130    
## neg_26_pd                            3.718e-02  1.414e-01    0.263 0.792632    
## neg_27_pd                           -2.152e-01  1.570e-01   -1.371 0.170645    
## neg_28_pd                           -2.102e-01  1.595e-01   -1.318 0.187786    
## neg_29_pd                            5.712e-03  1.686e-01    0.034 0.972974    
## neg_30_pd                           -6.349e-02  1.793e-01   -0.354 0.723254    
## neg_31_pd                           -7.353e-02  1.818e-01   -0.404 0.685918    
## neg_32_pd                           -5.692e-03  1.968e-01   -0.029 0.976933    
## neg_33_pd                            6.658e-02  2.498e-01    0.267 0.789851    
## pos_0_pd                            -2.301e-02  6.072e-02   -0.379 0.704770    
## pos_1_pd                            -5.961e-02  6.127e-02   -0.973 0.330724    
## pos_2_pd                            -2.841e-02  6.204e-02   -0.458 0.647008    
## pos_3_pd                            -6.438e-02  6.304e-02   -1.021 0.307267    
## pos_4_pd                            -6.953e-02  6.423e-02   -1.082 0.279202    
## pos_5_pd                            -1.105e-01  6.567e-02   -1.682 0.092724 .  
## pos_6_pd                            -1.105e-01  6.749e-02   -1.637 0.101807    
## pos_7_pd                            -1.066e-01  6.950e-02   -1.534 0.125178    
## pos_8_pd                            -1.617e-01  7.211e-02   -2.243 0.025007 *  
## pos_9_pd                            -1.812e-01  7.458e-02   -2.429 0.015225 *  
## pos_10_pd                           -1.955e-01  7.677e-02   -2.546 0.010965 *  
## pos_11_pd                           -1.992e-01  7.945e-02   -2.508 0.012236 *  
## pos_12_pd                           -2.016e-01  8.223e-02   -2.451 0.014333 *  
## pos_13_pd                           -2.705e-01  8.478e-02   -3.191 0.001444 ** 
## pos_14_pd                           -2.628e-01  8.835e-02   -2.975 0.002969 ** 
## pos_15_pd                           -2.708e-01  9.162e-02   -2.956 0.003159 ** 
## pos_16_pd                           -2.885e-01  9.454e-02   -3.051 0.002311 ** 
## pos_17_pd                           -2.850e-01  9.847e-02   -2.894 0.003851 ** 
## pos_18_pd                           -2.747e-01  1.020e-01   -2.694 0.007123 ** 
## pos_19_pd                           -2.633e-01  1.049e-01   -2.511 0.012133 *  
## pos_20_pd                           -2.747e-01  1.092e-01   -2.517 0.011935 *  
## pos_21_pd                           -3.075e-01  1.135e-01   -2.708 0.006830 ** 
## pos_22_pd                           -3.064e-01  1.171e-01   -2.617 0.008954 ** 
## pos_23_pd                           -3.240e-01  1.211e-01   -2.675 0.007548 ** 
## pos_24_pd                           -3.686e-01  1.266e-01   -2.911 0.003643 ** 
## pos_25_pd                           -3.300e-01  1.319e-01   -2.502 0.012447 *  
## pos_26_pd                           -3.265e-01  1.352e-01   -2.415 0.015810 *  
## pos_27_pd                           -3.660e-01  1.389e-01   -2.636 0.008465 ** 
## pos_28_pd                           -3.402e-01  1.420e-01   -2.395 0.016699 *  
## pos_29_pd                           -3.473e-01  1.495e-01   -2.323 0.020313 *  
## pos_30_pd                           -2.843e-01  1.542e-01   -1.844 0.065313 .  
## pos_31_pd                           -2.447e-01  1.595e-01   -1.534 0.125160    
## pos_32_pd                           -3.009e-01  1.696e-01   -1.774 0.076169 .  
## pos_33_pd                           -3.286e-01  1.760e-01   -1.867 0.062044 .  
## pos_34_pd                           -3.185e-01  1.793e-01   -1.777 0.075803 .  
## pos_35_pd                           -5.112e-01  1.958e-01   -2.611 0.009092 ** 
## pos_36_pd                           -5.411e-01  1.988e-01   -2.721 0.006568 ** 
## pos_37_pd                           -5.613e-01  2.208e-01   -2.542 0.011107 *  
## pos_38_pd                           -5.073e-01  2.698e-01   -1.880 0.060223 .  
## pos_39_pd                           -5.236e-01  2.725e-01   -1.921 0.054831 .  
## Time_Period_ID:RegionMidwest         8.336e-02  6.350e-03   13.128  < 2e-16 ***
## Time_Period_ID:RegionNortheast       6.990e-02  7.238e-03    9.657  < 2e-16 ***
## Time_Period_ID:RegionSouth           7.534e-02  6.113e-03   12.326  < 2e-16 ***
## Time_Period_ID:RegionWest            5.984e-02  6.325e-03    9.460  < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2)   -7.722e-04  1.317e-04   -5.865 5.29e-09 ***
## RegionNortheast:I(Time_Period_ID^2) -3.276e-04  1.529e-04   -2.142 0.032326 *  
## RegionSouth:I(Time_Period_ID^2)     -7.387e-04  1.228e-04   -6.017 2.13e-09 ***
## RegionWest:I(Time_Period_ID^2)      -6.900e-04  1.325e-04   -5.206 2.15e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.297 on 1863 degrees of freedom
## Multiple R-squared:  0.8471, Adjusted R-squared:  0.8359 
## F-statistic:  75.9 on 136 and 1863 DF,  p-value: < 2.2e-16

9.3.2 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_lin_time <-
  model.matrix(sensitivity_anlys_event_study_model_log_fixed_lin_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_event_study_log_fixed_lin_time <- coef(sensitivity_anlys_event_study_model_log_fixed_lin_time)
#type = "response" to get the estimated probabilities
sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time <- 
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_lin_time), 
                                                             log(sensitivity_anlys_event_study_data$prop_dead),
                                                             coefficient_values_sensitivity_anlys_event_study_log_fixed_lin_time,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_event_study_log_fixed_lin_time) - 50)
(sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time)
##                                           lb_coef   coef_values       ub_coef
## (Intercept)                         -1.089285e+01 -1.075211e+01 -1.061138e+01
## StateAlaska                          2.050016e-01  3.681466e-01  5.312917e-01
## StateArizona                         3.960676e-01  5.417212e-01  6.873748e-01
## StateArkansas                       -6.289267e-01 -5.238541e-01 -4.187814e-01
## StateCalifornia                      2.472627e-02  2.072651e-01  3.898039e-01
## StateColorado                        1.189345e-01  2.631204e-01  4.073063e-01
## StateConnecticut                    -1.382673e-01  9.640148e-02  3.310702e-01
## StateDelaware                       -1.978970e-06  1.370999e-01  2.742017e-01
## StateFlorida                         3.022941e-01  4.217490e-01  5.412040e-01
## StateGeorgia                         9.803159e-03  1.256264e-01  2.414496e-01
## StateHawaii                         -3.545868e-01 -1.939821e-01 -3.337747e-02
## StateIdaho                          -2.296005e-02  1.268318e-01  2.766236e-01
## StateIllinois                       -1.145279e-01  6.141792e-02  2.373637e-01
## StateIndiana                        -2.158224e-01 -7.032763e-02  7.516715e-02
## StateIowa                           -9.071543e-01 -7.573683e-01 -6.075824e-01
## StateKansas                         -4.940425e-01 -3.589045e-01 -2.237665e-01
## StateKentucky                        5.803174e-01  6.751092e-01  7.699011e-01
## StateLouisiana                       2.966035e-01  4.020635e-01  5.075235e-01
## StateMaine                          -3.073809e-01 -6.443333e-02  1.785142e-01
## StateMaryland                       -1.663525e+00 -1.450107e+00 -1.236689e+00
## StateMassachusetts                  -5.496039e-01 -2.099646e-01  1.296747e-01
## StateMichigan                       -2.243753e-01 -8.755277e-02  4.926972e-02
## StateMinnesota                      -9.512138e-01 -8.064512e-01 -6.616885e-01
## StateMississippi                    -2.173607e-01 -9.381424e-02  2.973222e-02
## StateMissouri                       -9.498085e-02  4.407434e-02  1.831295e-01
## StateMontana                        -2.617755e-01 -1.025779e-01  5.661976e-02
## StateNebraska                       -1.183936e+00 -1.044406e+00 -9.048764e-01
## StateNevada                          6.290268e-01  7.784794e-01  9.279319e-01
## StateNew Hampshire                  -2.286859e-01 -2.937945e-03  2.228100e-01
## StateNew Jersey                     -2.265469e-01  1.872191e-02  2.639907e-01
## StateNew Mexico                      7.189691e-01  8.850272e-01  1.051085e+00
## StateNew York                       -4.818839e-01 -2.568378e-01 -3.179176e-02
## StateNorth Carolina                  1.747784e-01  2.672113e-01  3.596442e-01
## StateNorth Dakota                   -1.510377e+00 -1.324860e+00 -1.139343e+00
## StateOhio                            2.792821e-01  4.498463e-01  6.204106e-01
## StateOklahoma                        3.296251e-01  4.439738e-01  5.583225e-01
## StateOregon                         -1.912956e-01 -4.696872e-02  9.735814e-02
## StatePennsylvania                    3.497080e-01  5.674613e-01  7.852145e-01
## StateRhode Island                   -8.254178e-01 -4.515446e-01 -7.767130e-02
## StateSouth Carolina                  4.291673e-02  1.590223e-01  2.751279e-01
## StateSouth Dakota                   -1.392377e+00 -1.233372e+00 -1.074367e+00
## StateTennessee                       3.771601e-01  4.661888e-01  5.552175e-01
## StateTexas                          -2.407234e-02  9.685755e-02  2.177874e-01
## StateUtah                            1.612987e-02  2.478713e-01  4.796127e-01
## StateVermont                        -5.828738e-01 -3.359903e-01 -8.910678e-02
## StateVirginia                       -6.377525e-02  3.640333e-02  1.365819e-01
## StateWashington                      1.422529e-01  2.882373e-01  4.342217e-01
## StateWest Virginia                   6.203789e-01  7.653531e-01  9.103272e-01
## StateWisconsin                      -2.231358e-01 -8.544359e-02  5.224862e-02
## StateWyoming                         1.008182e-01  2.722705e-01  4.437228e-01
## Naloxone_Pharmacy_Yes_Redefined     -5.203160e-03  5.742059e-02  1.200443e-01
## Naloxone_Pharmacy_No_Redefined      -4.396766e-02  1.750351e-02  7.897469e-02
## Medical_Marijuana_Redefined          1.483510e-01  2.179011e-01  2.874511e-01
## Recreational_Marijuana_Redefined    -1.550340e-01 -7.658036e-02  1.873229e-03
## GSL_Redefined                        6.228085e-03  5.951552e-02  1.128030e-01
## PDMP_Redefined                      -2.419083e-01 -1.878129e-01 -1.337176e-01
## Medicaid_Expansion_Redefined         2.919047e-02  7.905536e-02  1.289203e-01
## neg_2_pd                            -8.656997e-02  2.810796e-02  1.427859e-01
## neg_3_pd                            -8.212587e-02  3.165424e-02  1.454344e-01
## neg_4_pd                            -1.116155e-01  7.849767e-03  1.273150e-01
## neg_5_pd                            -1.122759e-01  3.931807e-03  1.201396e-01
## neg_6_pd                            -1.019467e-01  7.329461e-03  1.166056e-01
## neg_7_pd                            -1.541889e-01 -4.041923e-02  7.335044e-02
## neg_8_pd                            -2.464440e-01 -1.028469e-01  4.075008e-02
## neg_9_pd                            -1.839498e-01 -3.112932e-02  1.216912e-01
## neg_10_pd                           -1.256026e-01  1.448313e-02  1.545689e-01
## neg_11_pd                           -1.266113e-01  1.978697e-02  1.661852e-01
## neg_12_pd                           -4.910051e-02  1.119802e-01  2.730609e-01
## neg_13_pd                           -1.498086e-01  1.633347e-02  1.824756e-01
## neg_14_pd                           -1.667126e-01 -1.026441e-02  1.461838e-01
## neg_15_pd                           -2.440489e-01 -5.217270e-02  1.397035e-01
## neg_16_pd                           -2.159398e-01 -3.651798e-02  1.429038e-01
## neg_17_pd                           -1.932700e-01 -4.312360e-02  1.070228e-01
## neg_18_pd                           -1.807824e-01 -3.964077e-02  1.015009e-01
## neg_19_pd                           -3.791164e-01 -1.457109e-01  8.769464e-02
## neg_20_pd                           -4.528917e-01 -1.913222e-01  7.024731e-02
## neg_21_pd                           -3.065006e-01 -1.223277e-01  6.184521e-02
## neg_22_pd                           -2.967386e-01 -1.057079e-01  8.532286e-02
## neg_23_pd                           -4.106297e-01 -1.248126e-01  1.610045e-01
## neg_24_pd                           -5.206480e-01 -1.803116e-01  1.600248e-01
## neg_25_pd                           -3.255205e-01 -4.069763e-02  2.441253e-01
## neg_26_pd                           -3.168582e-01  3.718388e-02  3.912259e-01
## neg_27_pd                           -7.086401e-01 -2.151989e-01  2.782424e-01
## neg_28_pd                           -6.790181e-01 -2.102090e-01  2.586002e-01
## neg_29_pd                           -2.710709e-01  5.712051e-03  2.824950e-01
## neg_30_pd                           -3.072519e-01 -6.348969e-02  1.802726e-01
## neg_31_pd                           -2.716534e-01 -7.352839e-02  1.245966e-01
## neg_32_pd                           -1.928487e-01 -5.691465e-03  1.814658e-01
## neg_33_pd                           -2.064491e-01  6.658465e-02  3.396184e-01
## pos_0_pd                            -1.302889e-01 -2.301035e-02  8.426815e-02
## pos_1_pd                            -1.751046e-01 -5.961202e-02  5.588056e-02
## pos_2_pd                            -1.332546e-01 -2.841288e-02  7.642883e-02
## pos_3_pd                            -1.712859e-01 -6.437589e-02  4.253413e-02
## pos_4_pd                            -1.774399e-01 -6.952593e-02  3.838809e-02
## pos_5_pd                            -2.200513e-01 -1.104613e-01 -8.713108e-04
## pos_6_pd                            -2.245296e-01 -1.104797e-01  3.570095e-03
## pos_7_pd                            -2.250933e-01 -1.066177e-01  1.185801e-02
## pos_8_pd                            -2.753291e-01 -1.617419e-01 -4.815471e-02
## pos_9_pd                            -3.017241e-01 -1.811803e-01 -6.063641e-02
## pos_10_pd                           -3.186313e-01 -1.954766e-01 -7.232188e-02
## pos_11_pd                           -3.153751e-01 -1.992250e-01 -8.307492e-02
## pos_12_pd                           -3.233313e-01 -2.015583e-01 -7.978523e-02
## pos_13_pd                           -4.078027e-01 -2.704839e-01 -1.331650e-01
## pos_14_pd                           -4.029773e-01 -2.628264e-01 -1.226756e-01
## pos_15_pd                           -4.045901e-01 -2.707898e-01 -1.369896e-01
## pos_16_pd                           -4.280635e-01 -2.884658e-01 -1.488681e-01
## pos_17_pd                           -4.275803e-01 -2.849580e-01 -1.423356e-01
## pos_18_pd                           -4.185349e-01 -2.746873e-01 -1.308398e-01
## pos_19_pd                           -4.031417e-01 -2.632743e-01 -1.234069e-01
## pos_20_pd                           -4.231130e-01 -2.747120e-01 -1.263110e-01
## pos_21_pd                           -4.659699e-01 -3.074532e-01 -1.489365e-01
## pos_22_pd                           -4.630366e-01 -3.064491e-01 -1.498616e-01
## pos_23_pd                           -4.914538e-01 -3.239828e-01 -1.565117e-01
## pos_24_pd                           -5.457113e-01 -3.686145e-01 -1.915176e-01
## pos_25_pd                           -5.270883e-01 -3.300315e-01 -1.329747e-01
## pos_26_pd                           -5.178228e-01 -3.264909e-01 -1.351591e-01
## pos_27_pd                           -5.662755e-01 -3.659712e-01 -1.656668e-01
## pos_28_pd                           -5.474045e-01 -3.401865e-01 -1.329686e-01
## pos_29_pd                           -5.676360e-01 -3.472889e-01 -1.269419e-01
## pos_30_pd                           -5.115678e-01 -2.842876e-01 -5.700734e-02
## pos_31_pd                           -4.972488e-01 -2.446719e-01  7.904913e-03
## pos_32_pd                           -5.469828e-01 -3.009225e-01 -5.486222e-02
## pos_33_pd                           -6.272617e-01 -3.285532e-01 -2.984473e-02
## pos_34_pd                           -6.233627e-01 -3.184672e-01 -1.357177e-02
## pos_35_pd                           -7.761763e-01 -5.111925e-01 -2.462088e-01
## pos_36_pd                           -8.095707e-01 -5.410749e-01 -2.725791e-01
## pos_37_pd                           -8.184267e-01 -5.612764e-01 -3.041260e-01
## pos_38_pd                           -7.329770e-01 -5.073394e-01 -2.817017e-01
## pos_39_pd                           -8.075909e-01 -5.235895e-01 -2.395881e-01
## Time_Period_ID:RegionMidwest         7.397223e-02  8.336186e-02  9.275149e-02
## Time_Period_ID:RegionNortheast       4.962925e-02  6.989915e-02  9.016906e-02
## Time_Period_ID:RegionSouth           6.648278e-02  7.534090e-02  8.419902e-02
## Time_Period_ID:RegionWest            4.990702e-02  5.983841e-02  6.976980e-02
## RegionMidwest:I(Time_Period_ID^2)   -9.929257e-04 -7.722261e-04 -5.515265e-04
## RegionNortheast:I(Time_Period_ID^2) -7.565513e-04 -3.275860e-04  1.013793e-04
## RegionSouth:I(Time_Period_ID^2)     -9.541258e-04 -7.387434e-04 -5.233611e-04
## RegionWest:I(Time_Period_ID^2)      -9.292071e-04 -6.900113e-04 -4.508155e-04
##                                          sd_coef
## (Intercept)                         0.0718047299
## StateAlaska                         0.0832372748
## StateArizona                        0.0743130609
## StateArkansas                       0.0536084973
## StateCalifornia                     0.0931320602
## StateColorado                       0.0735642383
## StateConnecticut                    0.1197289584
## StateDelaware                       0.0699499164
## StateFlorida                        0.0609464175
## StateGeorgia                        0.0590934744
## StateHawaii                         0.0819411586
## StateIdaho                          0.0764244081
## StateIllinois                       0.0897682752
## StateIndiana                        0.0742320278
## StateIowa                           0.0764214032
## StateKansas                         0.0689479782
## StateKentucky                       0.0483631662
## StateLouisiana                      0.0538061113
## StateMaine                          0.1239528437
## StateMaryland                       0.1088867710
## StateMassachusetts                  0.1732853548
## StateMichigan                       0.0698073951
## StateMinnesota                      0.0738584885
## StateMississippi                    0.0630339094
## StateMissouri                       0.0709465264
## StateMontana                        0.0812232925
## StateNebraska                       0.0711886816
## StateNevada                         0.0762513103
## StateNew Hampshire                  0.1151775481
## StateNew Jersey                     0.1251371438
## StateNew Mexico                     0.0847235288
## StateNew York                       0.1148194152
## StateNorth Carolina                 0.0471596345
## StateNorth Dakota                   0.0946514407
## StateOhio                           0.0870225705
## StateOklahoma                       0.0583411725
## StateOregon                         0.0736361494
## StatePennsylvania                   0.1110986000
## StateRhode Island                   0.1907516664
## StateSouth Carolina                 0.0592375482
## StateSouth Dakota                   0.0811248893
## StateTennessee                      0.0454227853
## StateTexas                          0.0616989197
## StateUtah                           0.1182354224
## StateVermont                        0.1259609766
## StateVirginia                       0.0511115207
## StateWashington                     0.0744818207
## StateWest Virginia                  0.0739664162
## StateWisconsin                      0.0702511274
## StateWyoming                        0.0874756561
## Naloxone_Pharmacy_Yes_Redefined     0.0319508935
## Naloxone_Pharmacy_No_Redefined      0.0313628443
## Medical_Marijuana_Redefined         0.0354847320
## Recreational_Marijuana_Redefined    0.0400273424
## GSL_Redefined                       0.0271874677
## PDMP_Redefined                      0.0275996576
## Medicaid_Expansion_Redefined        0.0254412709
## neg_2_pd                            0.0585091490
## neg_3_pd                            0.0580510764
## neg_4_pd                            0.0609516608
## neg_5_pd                            0.0592896684
## neg_6_pd                            0.0557531504
## neg_7_pd                            0.0580457526
## neg_8_pd                            0.0732637884
## neg_9_pd                            0.0779696455
## neg_10_pd                           0.0714723204
## neg_11_pd                           0.0746929898
## neg_12_pd                           0.0821840333
## neg_13_pd                           0.0847663808
## neg_14_pd                           0.0798205026
## neg_15_pd                           0.0978960169
## neg_16_pd                           0.0915417272
## neg_17_pd                           0.0766053262
## neg_18_pd                           0.0720110493
## neg_19_pd                           0.1190844558
## neg_20_pd                           0.1334538192
## neg_21_pd                           0.0939657677
## neg_22_pd                           0.0974646494
## neg_23_pd                           0.1458250391
## neg_24_pd                           0.1736410354
## neg_25_pd                           0.1453178004
## neg_26_pd                           0.1806336937
## neg_27_pd                           0.2517557402
## neg_28_pd                           0.2391883334
## neg_29_pd                           0.1412158156
## neg_30_pd                           0.1243684913
## neg_31_pd                           0.1010841727
## neg_32_pd                           0.0954883973
## neg_33_pd                           0.1393029095
## pos_0_pd                            0.0547339304
## pos_1_pd                            0.0589247869
## pos_2_pd                            0.0534906706
## pos_3_pd                            0.0545459288
## pos_4_pd                            0.0550581698
## pos_5_pd                            0.0559132579
## pos_6_pd                            0.0581886948
## pos_7_pd                            0.0604467726
## pos_8_pd                            0.0579526492
## pos_9_pd                            0.0615019738
## pos_10_pd                           0.0628340417
## pos_11_pd                           0.0592602451
## pos_12_pd                           0.0621290999
## pos_13_pd                           0.0700606364
## pos_14_pd                           0.0715055328
## pos_15_pd                           0.0682654242
## pos_16_pd                           0.0712233271
## pos_17_pd                           0.0727665048
## pos_18_pd                           0.0733916212
## pos_19_pd                           0.0713609319
## pos_20_pd                           0.0757148028
## pos_21_pd                           0.0808758736
## pos_22_pd                           0.0798915755
## pos_23_pd                           0.0854444121
## pos_24_pd                           0.0903555345
## pos_25_pd                           0.1005391782
## pos_26_pd                           0.0976182739
## pos_27_pd                           0.1021960940
## pos_28_pd                           0.1057234454
## pos_29_pd                           0.1124219691
## pos_30_pd                           0.1159592983
## pos_31_pd                           0.1288657409
## pos_32_pd                           0.1255409744
## pos_33_pd                           0.1524022820
## pos_34_pd                           0.1555589153
## pos_35_pd                           0.1351957862
## pos_36_pd                           0.1369876529
## pos_37_pd                           0.1311991615
## pos_38_pd                           0.1151212479
## pos_39_pd                           0.1448986784
## Time_Period_ID:RegionMidwest        0.0047906273
## Time_Period_ID:RegionNortheast      0.0103417863
## Time_Period_ID:RegionSouth          0.0045194473
## Time_Period_ID:RegionWest           0.0050670362
## RegionMidwest:I(Time_Period_ID^2)   0.0001126018
## RegionNortheast:I(Time_Period_ID^2) 0.0002188598
## RegionSouth:I(Time_Period_ID^2)     0.0001098890
## RegionWest:I(Time_Period_ID^2)      0.0001220387
# write.csv(round(sensitivity_anlys_event_study_sd_and_ci, 3), "./Data/event_study_coef_and_ci.csv")

9.3.3 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_fixed_lin_time <- sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time %>%
  mutate(term = rownames(sensitivity_anlys_event_study_sd_and_ci_log_fixed_lin_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_fixed_lin_time) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study_log_fixed_lin_time, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

9.4 Event Study with Model SD

9.4.1 SD Estimator

summary_model_log_fixed_lin_time <- summary(sensitivity_anlys_event_study_model_log_fixed_lin_time)

coef_log_fixed_lin_time <- data.frame(coef_values = summary_model_log_fixed_lin_time$coefficients[,1],
                                      lb_coef = summary_model_log_fixed_lin_time$coefficients[,1] -
                                        1.96*summary_model_log_fixed_lin_time$coefficients[,2],
                                      ub_coef = summary_model_log_fixed_lin_time$coefficients[,1] +
                                        1.96*summary_model_log_fixed_lin_time$coefficients[,2])

9.4.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_event_study_log_fixed_lin_time_model_sd <- coef_log_fixed_lin_time %>%
  mutate(term = rownames(coef_log_fixed_lin_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}), 
                     sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")})))
colnames(plot_event_study_log_fixed_lin_time_model_sd) <- c("term", "estimate", "conf.low", "conf.high")

dwplot(plot_event_study_log_fixed_lin_time_model_sd, colour = "black",
       vars_order =  c(sapply((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0, 
                                   function(x){paste("pos_", x, "_pd", sep = "")}),
                       sapply(2:(max(merged_main_time_data_int$intervention_time_id, na.rm = TRUE) - 2), 
                                   function(x){paste("neg_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "States Excluded", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_hline(yintercept = 33, col = "red", linetype = "dashed")

9.5 Analysis With Only Periods After Treatment

formula_post_tx_log_fixed_lin_time <- formula(paste("log(prop_dead)~ State +
                                           Time_Period_ID:Region  +
                                           I(Time_Period_ID^2):Region + 
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_fixed_lin_time<-lm(formula_post_tx_log_fixed_lin_time,
                                         data = sensitivity_anlys_event_study_data)
summary(sensitivity_anlys_post_tx_model_log_fixed_lin_time)
## 
## Call:
## lm(formula = formula_post_tx_log_fixed_lin_time, data = sensitivity_anlys_event_study_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.02721 -0.13368  0.01535  0.15896  1.01698 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                         -1.080e+01  5.921e-02 -182.420  < 2e-16 ***
## StateAlaska                          2.967e-01  8.967e-02    3.309 0.000954 ***
## StateArizona                         4.987e-01  8.586e-02    5.808 7.40e-09 ***
## StateArkansas                       -5.591e-01  6.798e-02   -8.225 3.59e-16 ***
## StateCalifornia                      2.543e-01  9.219e-02    2.759 0.005853 ** 
## StateColorado                        2.249e-01  8.912e-02    2.524 0.011690 *  
## StateConnecticut                     1.058e-01  9.005e-02    1.175 0.240113    
## StateDelaware                        6.701e-02  7.023e-02    0.954 0.340179    
## StateFlorida                         4.733e-01  7.108e-02    6.658 3.62e-11 ***
## StateGeorgia                         1.862e-01  7.271e-02    2.561 0.010528 *  
## StateHawaii                         -2.335e-01  8.970e-02   -2.604 0.009294 ** 
## StateIdaho                           5.990e-02  8.696e-02    0.689 0.491038    
## StateIllinois                        1.075e-01  8.783e-02    1.225 0.220913    
## StateIndiana                        -8.394e-02  8.651e-02   -0.970 0.331978    
## StateIowa                           -7.274e-01  8.635e-02   -8.424  < 2e-16 ***
## StateKansas                         -3.463e-01  8.567e-02   -4.042 5.50e-05 ***
## StateKentucky                        6.379e-01  6.792e-02    9.392  < 2e-16 ***
## StateLouisiana                       4.279e-01  6.774e-02    6.317 3.32e-10 ***
## StateMaine                          -6.923e-02  9.276e-02   -0.746 0.455563    
## StateMaryland                       -1.409e+00  7.030e-02  -20.042  < 2e-16 ***
## StateMassachusetts                  -2.044e-01  8.995e-02   -2.273 0.023163 *  
## StateMichigan                       -6.756e-02  8.707e-02   -0.776 0.437842    
## StateMinnesota                      -7.958e-01  8.774e-02   -9.070  < 2e-16 ***
## StateMississippi                    -1.571e-01  6.783e-02   -2.316 0.020656 *  
## StateMissouri                        6.991e-02  8.739e-02    0.800 0.423777    
## StateMontana                        -7.476e-02  8.823e-02   -0.847 0.396923    
## StateNebraska                       -1.082e+00  8.754e-02  -12.362  < 2e-16 ***
## StateNevada                          7.920e-01  8.866e-02    8.933  < 2e-16 ***
## StateNew Hampshire                  -1.481e-02  8.975e-02   -0.165 0.868915    
## StateNew Jersey                      6.674e-02  9.089e-02    0.734 0.462820    
## StateNew Mexico                      8.669e-01  8.813e-02    9.836  < 2e-16 ***
## StateNew York                       -2.457e-01  8.967e-02   -2.740 0.006203 ** 
## StateNorth Carolina                  2.847e-01  6.712e-02    4.242 2.32e-05 ***
## StateNorth Dakota                   -1.364e+00  8.688e-02  -15.699  < 2e-16 ***
## StateOhio                            5.175e-01  8.962e-02    5.774 9.00e-09 ***
## StateOklahoma                        4.109e-01  6.754e-02    6.083 1.42e-09 ***
## StateOregon                         -6.071e-02  8.896e-02   -0.682 0.495062    
## StatePennsylvania                    6.255e-01  9.318e-02    6.713 2.52e-11 ***
## StateRhode Island                   -5.083e-01  9.098e-02   -5.587 2.64e-08 ***
## StateSouth Carolina                  8.840e-02  6.844e-02    1.292 0.196611    
## StateSouth Dakota                   -1.296e+00  8.821e-02  -14.690  < 2e-16 ***
## StateTennessee                       4.656e-01  6.645e-02    7.007 3.38e-12 ***
## StateTexas                           1.433e-01  7.069e-02    2.027 0.042752 *  
## StateUtah                            2.650e-01  8.636e-02    3.069 0.002177 ** 
## StateVermont                        -3.443e-01  9.008e-02   -3.822 0.000136 ***
## StateVirginia                        6.727e-02  6.809e-02    0.988 0.323272    
## StateWashington                      2.842e-01  8.938e-02    3.179 0.001500 ** 
## StateWest Virginia                   7.171e-01  6.823e-02   10.510  < 2e-16 ***
## StateWisconsin                      -5.121e-02  8.648e-02   -0.592 0.553788    
## StateWyoming                         2.618e-01  8.589e-02    3.048 0.002333 ** 
## Naloxone_Pharmacy_Yes_Redefined      5.810e-02  3.932e-02    1.478 0.139643    
## Naloxone_Pharmacy_No_Redefined       1.576e-02  3.864e-02    0.408 0.683337    
## Medical_Marijuana_Redefined          2.221e-01  3.123e-02    7.114 1.59e-12 ***
## Recreational_Marijuana_Redefined    -7.031e-02  4.881e-02   -1.440 0.149917    
## GSL_Redefined                        5.969e-02  3.161e-02    1.888 0.059123 .  
## PDMP_Redefined                      -1.832e-01  2.473e-02   -7.407 1.94e-13 ***
## Medicaid_Expansion_Redefined         7.554e-02  3.002e-02    2.517 0.011931 *  
## pos_0_pd                            -4.391e-02  4.635e-02   -0.948 0.343494    
## pos_1_pd                            -8.452e-02  4.681e-02   -1.805 0.071162 .  
## pos_2_pd                            -5.723e-02  4.729e-02   -1.210 0.226343    
## pos_3_pd                            -9.708e-02  4.785e-02   -2.029 0.042608 *  
## pos_4_pd                            -1.061e-01  4.845e-02   -2.189 0.028738 *  
## pos_5_pd                            -1.506e-01  4.925e-02   -3.057 0.002265 ** 
## pos_6_pd                            -1.542e-01  5.022e-02   -3.071 0.002165 ** 
## pos_7_pd                            -1.543e-01  5.111e-02   -3.019 0.002566 ** 
## pos_8_pd                            -2.137e-01  5.253e-02   -4.068 4.94e-05 ***
## pos_9_pd                            -2.373e-01  5.371e-02   -4.417 1.06e-05 ***
## pos_10_pd                           -2.554e-01  5.451e-02   -4.685 3.00e-06 ***
## pos_11_pd                           -2.633e-01  5.570e-02   -4.727 2.45e-06 ***
## pos_12_pd                           -2.699e-01  5.690e-02   -4.742 2.27e-06 ***
## pos_13_pd                           -3.427e-01  5.776e-02   -5.932 3.54e-09 ***
## pos_14_pd                           -3.391e-01  5.988e-02   -5.663 1.71e-08 ***
## pos_15_pd                           -3.515e-01  6.129e-02   -5.735 1.13e-08 ***
## pos_16_pd                           -3.731e-01  6.233e-02   -5.987 2.55e-09 ***
## pos_17_pd                           -3.741e-01  6.473e-02   -5.779 8.79e-09 ***
## pos_18_pd                           -3.678e-01  6.643e-02   -5.537 3.51e-08 ***
## pos_19_pd                           -3.599e-01  6.762e-02   -5.322 1.15e-07 ***
## pos_20_pd                           -3.754e-01  7.048e-02   -5.326 1.12e-07 ***
## pos_21_pd                           -4.122e-01  7.343e-02   -5.614 2.27e-08 ***
## pos_22_pd                           -4.150e-01  7.523e-02   -5.517 3.92e-08 ***
## pos_23_pd                           -4.370e-01  7.719e-02   -5.661 1.73e-08 ***
## pos_24_pd                           -4.847e-01  8.208e-02   -5.905 4.17e-09 ***
## pos_25_pd                           -4.491e-01  8.668e-02   -5.181 2.44e-07 ***
## pos_26_pd                           -4.496e-01  8.775e-02   -5.124 3.30e-07 ***
## pos_27_pd                           -4.935e-01  8.904e-02   -5.542 3.40e-08 ***
## pos_28_pd                           -4.711e-01  9.051e-02   -5.205 2.15e-07 ***
## pos_29_pd                           -4.818e-01  9.857e-02   -4.887 1.11e-06 ***
## pos_30_pd                           -4.227e-01  1.018e-01   -4.153 3.43e-05 ***
## pos_31_pd                           -3.879e-01  1.054e-01   -3.682 0.000238 ***
## pos_32_pd                           -4.492e-01  1.161e-01   -3.870 0.000113 ***
## pos_33_pd                           -4.813e-01  1.214e-01   -3.964 7.64e-05 ***
## pos_34_pd                           -4.751e-01  1.227e-01   -3.872 0.000111 ***
## pos_35_pd                           -6.716e-01  1.426e-01   -4.709 2.66e-06 ***
## pos_36_pd                           -7.051e-01  1.438e-01   -4.903 1.02e-06 ***
## pos_37_pd                           -7.306e-01  1.695e-01   -4.310 1.71e-05 ***
## pos_38_pd                           -6.815e-01  2.272e-01   -2.999 0.002742 ** 
## pos_39_pd                           -7.017e-01  2.282e-01   -3.074 0.002139 ** 
## Time_Period_ID:RegionMidwest         8.691e-02  5.282e-03   16.453  < 2e-16 ***
## Time_Period_ID:RegionNortheast       7.370e-02  6.058e-03   12.165  < 2e-16 ***
## Time_Period_ID:RegionSouth           7.974e-02  4.685e-03   17.022  < 2e-16 ***
## Time_Period_ID:RegionWest            6.430e-02  5.133e-03   12.528  < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2)   -7.645e-04  1.308e-04   -5.846 5.92e-09 ***
## RegionNortheast:I(Time_Period_ID^2) -3.293e-04  1.518e-04   -2.170 0.030138 *  
## RegionSouth:I(Time_Period_ID^2)     -7.483e-04  1.209e-04   -6.191 7.29e-10 ***
## RegionWest:I(Time_Period_ID^2)      -7.087e-04  1.313e-04   -5.397 7.61e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2967 on 1895 degrees of freedom
## Multiple R-squared:  0.8447, Adjusted R-squared:  0.8362 
## F-statistic: 99.13 on 104 and 1895 DF,  p-value: < 2.2e-16

9.5.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time <- model.matrix(sensitivity_anlys_post_tx_model_log_fixed_lin_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time <- coef(sensitivity_anlys_post_tx_model_log_fixed_lin_time)

sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time <-
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time), 
                                                         log(sensitivity_anlys_event_study_data$prop_dead),
                                                         coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time
##                                           lb_coef   coef_values       ub_coef
## (Intercept)                         -1.089784e+01 -1.080161e+01 -1.070539e+01
## StateAlaska                          1.377462e-01  2.967280e-01  4.557098e-01
## StateArizona                         3.572478e-01  4.986602e-01  6.400727e-01
## StateArkansas                       -6.645857e-01 -5.590763e-01 -4.535669e-01
## StateCalifornia                      8.192892e-02  2.543418e-01  4.267547e-01
## StateColorado                        8.411816e-02  2.249102e-01  3.657023e-01
## StateConnecticut                    -1.274304e-01  1.058193e-01  3.390691e-01
## StateDelaware                       -6.062897e-02  6.700585e-02  1.946407e-01
## StateFlorida                         3.655075e-01  4.732739e-01  5.810402e-01
## StateGeorgia                         8.581420e-02  1.861762e-01  2.865383e-01
## StateHawaii                         -3.790756e-01 -2.335472e-01 -8.801869e-02
## StateIdaho                          -8.147777e-02  5.990027e-02  2.012783e-01
## StateIllinois                       -6.146294e-02  1.075467e-01  2.765563e-01
## StateIndiana                        -2.298681e-01 -8.394337e-02  6.198141e-02
## StateIowa                           -8.706980e-01 -7.274116e-01 -5.841252e-01
## StateKansas                         -4.783749e-01 -3.463026e-01 -2.142302e-01
## StateKentucky                        5.483942e-01  6.378878e-01  7.273813e-01
## StateLouisiana                       3.277501e-01  4.278619e-01  5.279737e-01
## StateMaine                          -3.088537e-01 -6.923281e-02  1.703881e-01
## StateMaryland                       -1.611573e+00 -1.409027e+00 -1.206480e+00
## StateMassachusetts                  -5.388172e-01 -2.044092e-01  1.299989e-01
## StateMichigan                       -1.985843e-01 -6.756352e-02  6.345722e-02
## StateMinnesota                      -9.350398e-01 -7.958091e-01 -6.565784e-01
## StateMississippi                    -2.679502e-01 -1.571042e-01 -4.625827e-02
## StateMissouri                       -5.911046e-02  6.991381e-02  1.989381e-01
## StateMontana                        -2.247769e-01 -7.476100e-02  7.525488e-02
## StateNebraska                       -1.216469e+00 -1.082111e+00 -9.477529e-01
## StateNevada                          6.468741e-01  7.919969e-01  9.371197e-01
## StateNew Hampshire                  -2.404466e-01 -1.481407e-02  2.108185e-01
## StateNew Jersey                     -1.665574e-01  6.674317e-02  3.000437e-01
## StateNew Mexico                      7.068903e-01  8.668822e-01  1.026874e+00
## StateNew York                       -4.685869e-01 -2.456932e-01 -2.279944e-02
## StateNorth Carolina                  1.978452e-01  2.847260e-01  3.716067e-01
## StateNorth Dakota                   -1.546468e+00 -1.363971e+00 -1.181474e+00
## StateOhio                            3.605855e-01  5.174907e-01  6.743959e-01
## StateOklahoma                        3.010775e-01  4.108628e-01  5.206481e-01
## StateOregon                         -2.016273e-01 -6.070866e-02  8.020998e-02
## StatePennsylvania                    4.223253e-01  6.254850e-01  8.286446e-01
## StateRhode Island                   -9.035257e-01 -5.083039e-01 -1.130821e-01
## StateSouth Carolina                 -1.049984e-02  8.840328e-02  1.873064e-01
## StateSouth Dakota                   -1.456686e+00 -1.295833e+00 -1.134980e+00
## StateTennessee                       3.811316e-01  4.656090e-01  5.500865e-01
## StateTexas                           2.771875e-02  1.433278e-01  2.589369e-01
## StateUtah                            3.872767e-02  2.650449e-01  4.913622e-01
## StateVermont                        -5.901314e-01 -3.443276e-01 -9.852372e-02
## StateVirginia                       -2.766106e-02  6.727204e-02  1.622051e-01
## StateWashington                      1.419634e-01  2.841846e-01  4.264057e-01
## StateWest Virginia                   5.765619e-01  7.170779e-01  8.575938e-01
## StateWisconsin                      -1.786456e-01 -5.121088e-02  7.622383e-02
## StateWyoming                         9.222745e-02  2.618196e-01  4.314117e-01
## Naloxone_Pharmacy_Yes_Redefined     -3.675226e-03  5.810410e-02  1.198834e-01
## Naloxone_Pharmacy_No_Redefined      -4.544605e-02  1.576258e-02  7.697122e-02
## Medical_Marijuana_Redefined          1.514954e-01  2.221351e-01  2.927748e-01
## Recreational_Marijuana_Redefined    -1.458147e-01 -7.030772e-02  5.199212e-03
## GSL_Redefined                        7.240317e-03  5.969397e-02  1.121476e-01
## PDMP_Redefined                      -2.356820e-01 -1.831820e-01 -1.306820e-01
## Medicaid_Expansion_Redefined         2.548103e-02  7.554247e-02  1.256039e-01
## pos_0_pd                            -1.232220e-01 -4.391484e-02  3.539236e-02
## pos_1_pd                            -1.753316e-01 -8.451575e-02  6.300065e-03
## pos_2_pd                            -1.345725e-01 -5.723292e-02  2.010664e-02
## pos_3_pd                            -1.767463e-01 -9.707618e-02 -1.740610e-02
## pos_4_pd                            -1.864027e-01 -1.060528e-01 -2.570288e-02
## pos_5_pd                            -2.338331e-01 -1.505587e-01 -6.728426e-02
## pos_6_pd                            -2.431210e-01 -1.542152e-01 -6.530942e-02
## pos_7_pd                            -2.484738e-01 -1.543273e-01 -6.018072e-02
## pos_8_pd                            -3.019100e-01 -2.136631e-01 -1.254163e-01
## pos_9_pd                            -3.339051e-01 -2.372509e-01 -1.405966e-01
## pos_10_pd                           -3.551988e-01 -2.553866e-01 -1.555745e-01
## pos_11_pd                           -3.537798e-01 -2.633042e-01 -1.728287e-01
## pos_12_pd                           -3.681921e-01 -2.698599e-01 -1.715278e-01
## pos_13_pd                           -4.602296e-01 -3.426755e-01 -2.251215e-01
## pos_14_pd                           -4.594010e-01 -3.390926e-01 -2.187843e-01
## pos_15_pd                           -4.618573e-01 -3.515039e-01 -2.411505e-01
## pos_16_pd                           -4.903779e-01 -3.731365e-01 -2.558951e-01
## pos_17_pd                           -4.941843e-01 -3.740702e-01 -2.539562e-01
## pos_18_pd                           -4.878219e-01 -3.678096e-01 -2.477973e-01
## pos_19_pd                           -4.749640e-01 -3.599141e-01 -2.448642e-01
## pos_20_pd                           -4.986432e-01 -3.754216e-01 -2.522001e-01
## pos_21_pd                           -5.463634e-01 -4.122110e-01 -2.780585e-01
## pos_22_pd                           -5.478495e-01 -4.150284e-01 -2.822073e-01
## pos_23_pd                           -5.794203e-01 -4.369711e-01 -2.945219e-01
## pos_24_pd                           -6.367526e-01 -4.846949e-01 -3.326372e-01
## pos_25_pd                           -6.223804e-01 -4.491097e-01 -2.758390e-01
## pos_26_pd                           -6.176132e-01 -4.496148e-01 -2.816163e-01
## pos_27_pd                           -6.721251e-01 -4.934802e-01 -3.148352e-01
## pos_28_pd                           -6.582506e-01 -4.710687e-01 -2.838869e-01
## pos_29_pd                           -6.826784e-01 -4.817697e-01 -2.808610e-01
## pos_30_pd                           -6.304967e-01 -4.227249e-01 -2.149530e-01
## pos_31_pd                           -6.222924e-01 -3.878906e-01 -1.534888e-01
## pos_32_pd                           -6.725618e-01 -4.492206e-01 -2.258793e-01
## pos_33_pd                           -7.607229e-01 -4.813352e-01 -2.019476e-01
## pos_34_pd                           -7.603424e-01 -4.751498e-01 -1.899573e-01
## pos_35_pd                           -9.116375e-01 -6.715534e-01 -4.314694e-01
## pos_36_pd                           -9.468931e-01 -7.050687e-01 -4.632442e-01
## pos_37_pd                           -9.597621e-01 -7.305666e-01 -5.013711e-01
## pos_38_pd                           -8.739929e-01 -6.815169e-01 -4.890408e-01
## pos_39_pd                           -9.575988e-01 -7.016723e-01 -4.457458e-01
## Time_Period_ID:RegionMidwest         7.736058e-02  8.691258e-02  9.646458e-02
## Time_Period_ID:RegionNortheast       5.286972e-02  7.369820e-02  9.452667e-02
## Time_Period_ID:RegionSouth           7.141658e-02  7.974451e-02  8.807245e-02
## Time_Period_ID:RegionWest            5.475924e-02  6.430477e-02  7.385029e-02
## RegionMidwest:I(Time_Period_ID^2)   -9.870165e-04 -7.645227e-04 -5.420290e-04
## RegionNortheast:I(Time_Period_ID^2) -7.629619e-04 -3.292992e-04  1.043635e-04
## RegionSouth:I(Time_Period_ID^2)     -9.583733e-04 -7.482645e-04 -5.381557e-04
## RegionWest:I(Time_Period_ID^2)      -9.404291e-04 -7.087475e-04 -4.770660e-04
##                                          sd_coef
## (Intercept)                         0.0490957400
## StateAlaska                         0.0811131627
## StateArizona                        0.0721492324
## StateArkansas                       0.0538313336
## StateCalifornia                     0.0879657491
## StateColorado                       0.0718326767
## StateConnecticut                    0.1190049832
## StateDelaware                       0.0651198065
## StateFlorida                        0.0549828165
## StateGeorgia                        0.0512051164
## StateHawaii                         0.0742492201
## StateIdaho                          0.0721316506
## StateIllinois                       0.0862293965
## StateIndiana                        0.0744514193
## StateIowa                           0.0731052897
## StateKansas                         0.0673838653
## StateKentucky                       0.0456599777
## StateLouisiana                      0.0510774544
## StateMaine                          0.1222555731
## StateMaryland                       0.1033398255
## StateMassachusetts                  0.1706163396
## StateMichigan                       0.0668473155
## StateMinnesota                      0.0710360630
## StateMississippi                    0.0565540664
## StateMissouri                       0.0658287065
## StateMontana                        0.0765387171
## StateNebraska                       0.0685499310
## StateNevada                         0.0740422480
## StateNew Hampshire                  0.1151186308
## StateNew Jersey                     0.1190308921
## StateNew Mexico                     0.0816284883
## StateNew York                       0.1137212858
## StateNorth Carolina                 0.0443269227
## StateNorth Dakota                   0.0931106490
## StateOhio                           0.0800536790
## StateOklahoma                       0.0560129333
## StateOregon                         0.0718972637
## StatePennsylvania                   0.1036528910
## StateRhode Island                   0.2016437652
## StateSouth Carolina                 0.0504607762
## StateSouth Dakota                   0.0820679025
## StateTennessee                      0.0431007348
## StateTexas                          0.0589842209
## StateUtah                           0.1154679802
## StateVermont                        0.1254101229
## StateVirginia                       0.0484352568
## StateWashington                     0.0725617948
## StateWest Virginia                  0.0716918186
## StateWisconsin                      0.0650177061
## StateWyoming                        0.0865265942
## Naloxone_Pharmacy_Yes_Redefined     0.0315200643
## Naloxone_Pharmacy_No_Redefined      0.0312288969
## Medical_Marijuana_Redefined         0.0360406637
## Recreational_Marijuana_Redefined    0.0385239472
## GSL_Redefined                       0.0267620668
## PDMP_Redefined                      0.0267857235
## Medicaid_Expansion_Redefined        0.0255415494
## pos_0_pd                            0.0404628545
## pos_1_pd                            0.0463346019
## pos_2_pd                            0.0394589631
## pos_3_pd                            0.0406479982
## pos_4_pd                            0.0409948418
## pos_5_pd                            0.0424869393
## pos_6_pd                            0.0453600901
## pos_7_pd                            0.0480339467
## pos_8_pd                            0.0450239010
## pos_9_pd                            0.0493133927
## pos_10_pd                           0.0509245689
## pos_11_pd                           0.0461609957
## pos_12_pd                           0.0501694689
## pos_13_pd                           0.0599765576
## pos_14_pd                           0.0613818152
## pos_15_pd                           0.0563027514
## pos_16_pd                           0.0598170316
## pos_17_pd                           0.0612826655
## pos_18_pd                           0.0612307741
## pos_19_pd                           0.0586989247
## pos_20_pd                           0.0628681264
## pos_21_pd                           0.0684451285
## pos_22_pd                           0.0677658707
## pos_23_pd                           0.0726781649
## pos_24_pd                           0.0775804629
## pos_25_pd                           0.0884034189
## pos_26_pd                           0.0857135144
## pos_27_pd                           0.0911453894
## pos_28_pd                           0.0955009363
## pos_29_pd                           0.1025044471
## pos_30_pd                           0.1060060398
## pos_31_pd                           0.1195927353
## pos_32_pd                           0.1139496052
## pos_33_pd                           0.1425447070
## pos_34_pd                           0.1455064070
## pos_35_pd                           0.1224918631
## pos_36_pd                           0.1233798189
## pos_37_pd                           0.1169364617
## pos_38_pd                           0.0982020642
## pos_39_pd                           0.1305747399
## Time_Period_ID:RegionMidwest        0.0048734711
## Time_Period_ID:RegionNortheast      0.0106267742
## Time_Period_ID:RegionSouth          0.0042489462
## Time_Period_ID:RegionWest           0.0048701665
## RegionMidwest:I(Time_Period_ID^2)   0.0001135172
## RegionNortheast:I(Time_Period_ID^2) 0.0002212565
## RegionSouth:I(Time_Period_ID^2)     0.0001071984
## RegionWest:I(Time_Period_ID^2)      0.0001182049

9.5.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_lin_time <- sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_fixed_lin_time) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_lin_time$num_states <- sapply(plot_post_tx_log_fixed_lin_time$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx_log_fixed_lin_time, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() 

  # geom_vline(aes(xintercept = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]), 
  #            linetype = "dashed", color = "red") 
  # geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]), y = 12, 
  #           x = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"] + 0.1), color = "red")
  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

9.5.3 Attributable Deaths

date_data <- sensitivity_anlys_event_study_data[, c("Time_Period_ID", "Time_Period_Start")]
date_data <- date_data[!duplicated(date_data),]
attr_deaths_est_log_lin_time_diff_post_tx <- attr_death_compute(sensitivity_anlys_event_study_data,
                                                   sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time, 
                                                   post_tx_model = TRUE)
attr_deaths_est_log_lin_time_diff_post_tx <- merge(attr_deaths_est_log_lin_time_diff_post_tx, date_data, 
                                                    by.x = "Time_Period", by.y = "Time_Period_ID")

ggplot(attr_deaths_est_log_lin_time_diff_post_tx, aes(x = Time_Period_Start)) + 
  # geom_point(aes(y = attr_deaths)) + 
  geom_line(aes(y = attr_deaths, linetype = "Estimate")) + 
  # geom_point(aes(y = attr_deaths_lb)) + 
  geom_line(aes(y = attr_deaths_lb, linetype = "95% CI")) + 
  # geom_point(aes(y = attr_deaths_ub)) + 
  geom_line(aes(y = attr_deaths_ub, linetype = "95% CI")) + 
  labs(x = "Date", y = "Attributable Deaths",
       title = "Estimated Number of Attributable Deaths Using Linear and Quad. Time Effects, 
       Log Probability of Drug Overdose Death, Linear Policy Effects",
       linetype = "") + 
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black")) + 
  scale_linetype_manual(values = c("dashed", "solid"))

9.6 Analysis With Only Periods After Treatment with Model SD

summary_model_log_fixed_lin_time_post_tx_model_sd <- summary(sensitivity_anlys_post_tx_model_log_fixed_lin_time)

coef_log_fixed_lin_time_post_tx_model_sd <- data.frame(coef_values = summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,1],
                                      lb_coef = summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,1] -
                                        1.96*summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,2],
                                      ub_coef = summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,1] +
                                        1.96*summary_model_log_fixed_lin_time_post_tx_model_sd$coefficients[,2])

9.6.1 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_lin_time_model_sd <- coef_log_fixed_lin_time_post_tx_model_sd %>%
  mutate(term = rownames(coef_log_fixed_lin_time_post_tx_model_sd)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_fixed_lin_time_model_sd) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_lin_time_model_sd$num_states <- sapply(plot_post_tx_log_fixed_lin_time_model_sd$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})

dwplot(plot_post_tx_log_fixed_lin_time_model_sd, colour = "black",
       vars_order =  c(sapply(((max(merged_main_time_data_int$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)):0), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) +  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4)) +
  geom_vline(aes(xintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods") + 
  scale_color_grey() + 
  coord_flip() +
  geom_vline(aes(xintercept = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]), 
             linetype = "dashed", color = "red") +
  geom_text(aes(label = paste("Coefficient Estimate: ", coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"]), y = 12, 
            x = coef(main_analysis_model_log_fixed_lin_time)["Intervention_Redefined"] + 0.1), color = "red")

  # geom_text(aes(label = num_states, x = .1, y = 40:1), size = 2)

9.7 Analysis With Only Periods After Treatment Subset

formula_post_tx_log_fixed_lin_time <- formula(paste("log(prop_dead)~ State +
                                           Time_Period_ID:Region  +
                                           I(Time_Period_ID^2):Region + 
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +",
                                     paste(sapply(0:(29 - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)),
                              function(x)paste("pos_", x, "_pd", sep = "")), collapse = "+")))
#run the gam model
sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset<-lm(formula_post_tx_log_fixed_lin_time,
                                         data = data_subset)
summary(sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset)
## 
## Call:
## lm(formula = formula_post_tx_log_fixed_lin_time, data = data_subset)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.95559 -0.12809  0.00672  0.14870  1.08300 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                         -1.091e+01  7.112e-02 -153.373  < 2e-16 ***
## StateAlaska                          4.274e-01  1.082e-01    3.948 8.27e-05 ***
## StateArizona                         6.058e-01  1.027e-01    5.896 4.70e-09 ***
## StateArkansas                       -5.290e-01  8.071e-02   -6.555 7.91e-11 ***
## StateCalifornia                      4.080e-01  1.133e-01    3.599 0.000330 ***
## StateColorado                        3.136e-01  1.078e-01    2.910 0.003675 ** 
## StateConnecticut                     1.860e-01  1.110e-01    1.676 0.094028 .  
## StateDelaware                        7.298e-02  8.169e-02    0.893 0.371820    
## StateFlorida                         5.434e-01  8.480e-02    6.408 2.03e-10 ***
## StateGeorgia                         2.321e-01  8.730e-02    2.658 0.007943 ** 
## StateHawaii                         -1.280e-01  1.078e-01   -1.187 0.235427    
## StateIdaho                           1.331e-01  1.045e-01    1.274 0.202961    
## StateIllinois                        3.728e-01  1.079e-01    3.457 0.000564 ***
## StateIndiana                        -7.394e-02  1.042e-01   -0.709 0.478242    
## StateIowa                           -6.737e-01  1.039e-01   -6.485 1.24e-10 ***
## StateKansas                         -2.381e-01  1.032e-01   -2.308 0.021175 *  
## StateKentucky                        7.202e-01  8.074e-02    8.920  < 2e-16 ***
## StateLouisiana                       4.539e-01  8.056e-02    5.635 2.13e-08 ***
## StateMaine                          -1.110e-01  1.123e-01   -0.988 0.323235    
## StateMaryland                       -1.668e+00  8.458e-02  -19.717  < 2e-16 ***
## StateMassachusetts                  -3.474e-01  1.085e-01   -3.202 0.001395 ** 
## StateMichigan                        5.662e-03  1.047e-01    0.054 0.956866    
## StateMinnesota                      -6.910e-01  1.064e-01   -6.497 1.15e-10 ***
## StateMississippi                    -1.118e-02  8.047e-02   -0.139 0.889558    
## StateMissouri                        1.442e-01  1.046e-01    1.379 0.168134    
## StateMontana                        -8.668e-04  1.064e-01   -0.008 0.993499    
## StateNebraska                       -9.949e-01  1.046e-01   -9.511  < 2e-16 ***
## StateNevada                          9.338e-01  1.074e-01    8.697  < 2e-16 ***
## StateNew Hampshire                  -9.882e-02  1.088e-01   -0.909 0.363676    
## StateNew Jersey                      7.787e-02  1.111e-01    0.701 0.483460    
## StateNew Mexico                      1.095e+00  1.109e-01    9.877  < 2e-16 ***
## StateNew York                       -1.430e-01  1.098e-01   -1.302 0.193240    
## StateNorth Carolina                  3.184e-01  8.021e-02    3.969 7.58e-05 ***
## StateNorth Dakota                   -1.353e+00  1.042e-01  -12.985  < 2e-16 ***
## StateOhio                            5.141e-01  1.085e-01    4.738 2.38e-06 ***
## StateOklahoma                        5.687e-01  8.039e-02    7.074 2.41e-12 ***
## StateOregon                          4.517e-02  1.076e-01    0.420 0.674651    
## StatePennsylvania                    6.673e-01  1.135e-01    5.880 5.17e-09 ***
## StateRhode Island                   -6.474e-01  1.097e-01   -5.902 4.54e-09 ***
## StateSouth Carolina                  1.539e-01  8.050e-02    1.912 0.056077 .  
## StateSouth Dakota                   -1.220e+00  1.048e-01  -11.639  < 2e-16 ***
## StateTennessee                       4.655e-01  7.933e-02    5.868 5.53e-09 ***
## StateTexas                           2.892e-01  8.417e-02    3.435 0.000609 ***
## StateUtah                            1.571e-01  1.048e-01    1.499 0.134152    
## StateVermont                        -2.941e-01  1.095e-01   -2.687 0.007304 ** 
## StateVirginia                        7.035e-02  8.128e-02    0.865 0.386951    
## StateWashington                      4.252e-01  1.084e-01    3.922 9.24e-05 ***
## StateWest Virginia                   7.256e-01  8.082e-02    8.977  < 2e-16 ***
## StateWisconsin                      -2.257e-02  1.043e-01   -0.216 0.828759    
## StateWyoming                         2.713e-01  1.032e-01    2.628 0.008678 ** 
## Naloxone_Pharmacy_Yes_Redefined     -2.196e-01  8.264e-02   -2.657 0.007983 ** 
## Naloxone_Pharmacy_No_Redefined      -5.699e-02  5.770e-02   -0.988 0.323514    
## Medical_Marijuana_Redefined          2.086e-01  4.261e-02    4.896 1.10e-06 ***
## Recreational_Marijuana_Redefined    -1.168e-01  1.470e-01   -0.794 0.427066    
## GSL_Redefined                        6.460e-02  5.194e-02    1.244 0.213825    
## PDMP_Redefined                      -1.947e-01  2.904e-02   -6.703 2.99e-11 ***
## Medicaid_Expansion_Redefined        -5.890e-03  5.491e-02   -0.107 0.914591    
## pos_0_pd                            -2.189e-02  5.020e-02   -0.436 0.662773    
## pos_1_pd                            -9.194e-02  5.114e-02   -1.798 0.072462 .  
## pos_2_pd                            -5.145e-02  5.171e-02   -0.995 0.319958    
## pos_3_pd                            -1.057e-01  5.395e-02   -1.959 0.050289 .  
## pos_4_pd                            -1.077e-01  5.524e-02   -1.949 0.051469 .  
## pos_5_pd                            -1.383e-01  5.631e-02   -2.457 0.014145 *  
## pos_6_pd                            -1.596e-01  5.854e-02   -2.726 0.006484 ** 
## pos_7_pd                            -1.415e-01  5.990e-02   -2.362 0.018309 *  
## pos_8_pd                            -1.719e-01  6.097e-02   -2.820 0.004877 ** 
## pos_9_pd                            -2.089e-01  6.408e-02   -3.260 0.001144 ** 
## pos_10_pd                           -2.369e-01  6.715e-02   -3.528 0.000433 ***
## pos_11_pd                           -2.205e-01  6.875e-02   -3.208 0.001369 ** 
## pos_12_pd                           -2.408e-01  7.062e-02   -3.409 0.000670 ***
## pos_13_pd                           -3.672e-01  7.589e-02   -4.839 1.46e-06 ***
## pos_14_pd                           -3.699e-01  8.075e-02   -4.582 5.04e-06 ***
## pos_15_pd                           -2.912e-01  8.176e-02   -3.562 0.000381 ***
## pos_16_pd                           -3.257e-01  8.293e-02   -3.928 9.00e-05 ***
## pos_17_pd                           -3.436e-01  8.422e-02   -4.080 4.77e-05 ***
## pos_18_pd                           -3.463e-01  9.277e-02   -3.732 0.000197 ***
## pos_19_pd                           -3.135e-01  9.645e-02   -3.251 0.001180 ** 
## pos_20_pd                           -3.141e-01  1.001e-01   -3.137 0.001744 ** 
## pos_21_pd                           -3.555e-01  1.119e-01   -3.179 0.001513 ** 
## pos_22_pd                           -3.704e-01  1.182e-01   -3.135 0.001757 ** 
## pos_23_pd                           -4.075e-01  1.207e-01   -3.375 0.000759 ***
## pos_24_pd                           -5.288e-01  1.401e-01   -3.776 0.000166 ***
## pos_25_pd                           -5.278e-01  1.418e-01   -3.723 0.000205 ***
## pos_26_pd                           -4.619e-01  1.683e-01   -2.745 0.006125 ** 
## pos_27_pd                           -4.197e-01  2.287e-01   -1.835 0.066675 .  
## pos_28_pd                           -2.417e-01  2.324e-01   -1.040 0.298510    
## Time_Period_ID:RegionMidwest         9.416e-02  8.216e-03   11.461  < 2e-16 ***
## Time_Period_ID:RegionNortheast       1.020e-01  9.695e-03   10.516  < 2e-16 ***
## Time_Period_ID:RegionSouth           9.537e-02  7.201e-03   13.245  < 2e-16 ***
## Time_Period_ID:RegionWest            6.822e-02  8.059e-03    8.466  < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2)   -1.007e-03  2.684e-04   -3.752 0.000183 ***
## RegionNortheast:I(Time_Period_ID^2) -1.307e-03  3.224e-04   -4.055 5.30e-05 ***
## RegionSouth:I(Time_Period_ID^2)     -1.301e-03  2.341e-04   -5.557 3.30e-08 ***
## RegionWest:I(Time_Period_ID^2)      -7.723e-04  2.652e-04   -2.912 0.003647 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3015 on 1356 degrees of freedom
## Multiple R-squared:  0.8225, Adjusted R-squared:  0.8104 
## F-statistic: 67.58 on 93 and 1356 DF,  p-value: < 2.2e-16

9.7.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time_subset <-
  model.matrix(sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time_subset <- coef(sensitivity_anlys_post_tx_model_log_fixed_lin_time_subset)

sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset <-
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time_subset), 
                                                         log(data_subset$prop_dead),
                                                         coefficient_values_sensitivity_anlys_post_tx_log_fixed_lin_time_subset,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_post_tx_log_fixed_lin_time_subset) - 50)
sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset
##                                           lb_coef   coef_values       ub_coef
## (Intercept)                         -11.023282693 -1.090742e+01 -1.079156e+01
## StateAlaska                           0.235133487  4.273972e-01  6.196609e-01
## StateArizona                          0.437914755  6.057654e-01  7.736160e-01
## StateArkansas                        -0.667087310 -5.290018e-01 -3.909163e-01
## StateCalifornia                       0.195843512  4.079544e-01  6.200652e-01
## StateColorado                         0.143067848  3.136282e-01  4.841886e-01
## StateConnecticut                     -0.093702482  1.859977e-01  4.656978e-01
## StateDelaware                        -0.073053160  7.297514e-02  2.190034e-01
## StateFlorida                          0.416674394  5.433858e-01  6.700972e-01
## StateGeorgia                          0.107944895  2.320893e-01  3.562337e-01
## StateHawaii                          -0.302227812 -1.279554e-01  4.631692e-02
## StateIdaho                           -0.037281975  1.330894e-01  3.034608e-01
## StateIllinois                         0.189126809  3.728130e-01  5.564992e-01
## StateIndiana                         -0.242052887 -7.393566e-02  9.418157e-02
## StateIowa                            -0.845782838 -6.736635e-01 -5.015441e-01
## StateKansas                          -0.393312824 -2.380811e-01 -8.284935e-02
## StateKentucky                         0.610068000  7.201852e-01  8.303024e-01
## StateLouisiana                        0.328483962  4.539403e-01  5.793965e-01
## StateMaine                           -0.395633347 -1.109917e-01  1.736500e-01
## StateMaryland                        -1.864276094 -1.667625e+00 -1.470974e+00
## StateMassachusetts                   -0.725762517 -3.474105e-01  3.094145e-02
## StateMichigan                        -0.149674005  5.662479e-03  1.609990e-01
## StateMinnesota                       -0.857653068 -6.909765e-01 -5.243000e-01
## StateMississippi                     -0.127799183 -1.117615e-02  1.054469e-01
## StateMissouri                        -0.003744441  1.442237e-01  2.921917e-01
## StateMontana                         -0.173522996 -8.668399e-04  1.717893e-01
## StateNebraska                        -1.153801789 -9.949016e-01 -8.360015e-01
## StateNevada                           0.763365368  9.337537e-01  1.104142e+00
## StateNew Hampshire                   -0.355206774 -9.882452e-02  1.575577e-01
## StateNew Jersey                      -0.210474548  7.787446e-02  3.662235e-01
## StateNew Mexico                       0.894942772  1.095285e+00  1.295628e+00
## StateNew York                        -0.406006599 -1.429667e-01  1.200732e-01
## StateNorth Carolina                   0.215166203  3.183710e-01  4.215758e-01
## StateNorth Dakota                    -1.586142779 -1.353422e+00 -1.120701e+00
## StateOhio                             0.330259428  5.141044e-01  6.979494e-01
## StateOklahoma                         0.459256321  5.686696e-01  6.780828e-01
## StateOregon                          -0.124807899  4.516508e-02  2.151381e-01
## StatePennsylvania                     0.414552073  6.672716e-01  9.199911e-01
## StateRhode Island                    -1.111525296 -6.473864e-01 -1.832475e-01
## StateSouth Carolina                   0.035379721  1.539228e-01  2.724658e-01
## StateSouth Dakota                    -1.406996687 -1.219749e+00 -1.032501e+00
## StateTennessee                        0.360290983  4.655087e-01  5.707264e-01
## StateTexas                            0.163471204  2.891574e-01  4.148436e-01
## StateUtah                            -0.092235213  1.571495e-01  4.065341e-01
## StateVermont                         -0.581440694 -2.941311e-01 -6.821537e-03
## StateVirginia                        -0.048848333  7.034543e-02  1.895392e-01
## StateWashington                       0.253603664  4.252324e-01  5.968611e-01
## StateWest Virginia                    0.546578326  7.255767e-01  9.045750e-01
## StateWisconsin                       -0.173940655 -2.256830e-02  1.288040e-01
## StateWyoming                          0.077279857  2.712827e-01  4.652855e-01
## Naloxone_Pharmacy_Yes_Redefined      -0.326260650 -2.195564e-01 -1.128522e-01
## Naloxone_Pharmacy_No_Redefined       -0.176146117 -5.698786e-02  6.217040e-02
## Medical_Marijuana_Redefined           0.100694356  2.085979e-01  3.165014e-01
## Recreational_Marijuana_Redefined     -0.255121399 -1.167887e-01  2.154391e-02
## GSL_Redefined                        -0.036003519  6.460321e-02  1.652099e-01
## PDMP_Redefined                       -0.249753144 -1.946791e-01 -1.396051e-01
## Medicaid_Expansion_Redefined         -0.101143723 -5.890220e-03  8.936328e-02
## pos_0_pd                             -0.110293146 -2.189486e-02  6.650342e-02
## pos_1_pd                             -0.189497204 -9.193815e-02  5.620896e-03
## pos_2_pd                             -0.131970698 -5.144947e-02  2.907176e-02
## pos_3_pd                             -0.187587554 -1.057042e-01 -2.382087e-02
## pos_4_pd                             -0.186343571 -1.076845e-01 -2.902539e-02
## pos_5_pd                             -0.225007960 -1.383359e-01 -5.166387e-02
## pos_6_pd                             -0.254856094 -1.595957e-01 -6.433526e-02
## pos_7_pd                             -0.243459495 -1.414953e-01 -3.953115e-02
## pos_8_pd                             -0.265077022 -1.719037e-01 -7.873044e-02
## pos_9_pd                             -0.316981488 -2.088760e-01 -1.007705e-01
## pos_10_pd                            -0.353466894 -2.368807e-01 -1.202946e-01
## pos_11_pd                            -0.326600183 -2.205425e-01 -1.144847e-01
## pos_12_pd                            -0.364619662 -2.407627e-01 -1.169057e-01
## pos_13_pd                            -0.537125144 -3.671995e-01 -1.972739e-01
## pos_14_pd                            -0.551658895 -3.699445e-01 -1.882301e-01
## pos_15_pd                            -0.418529692 -2.912092e-01 -1.638887e-01
## pos_16_pd                            -0.467576839 -3.257402e-01 -1.839035e-01
## pos_17_pd                            -0.493181543 -3.435766e-01 -1.939717e-01
## pos_18_pd                            -0.510248067 -3.462708e-01 -1.822935e-01
## pos_19_pd                            -0.473693631 -3.135105e-01 -1.533274e-01
## pos_20_pd                            -0.491357096 -3.141007e-01 -1.368444e-01
## pos_21_pd                            -0.591164622 -3.555464e-01 -1.199282e-01
## pos_22_pd                            -0.633488273 -3.703993e-01 -1.073104e-01
## pos_23_pd                            -0.659211093 -4.074668e-01 -1.557224e-01
## pos_24_pd                            -0.735178991 -5.288245e-01 -3.224701e-01
## pos_25_pd                            -0.732526295 -5.278271e-01 -3.231279e-01
## pos_26_pd                            -0.719857242 -4.619416e-01 -2.040259e-01
## pos_27_pd                            -0.639431412 -4.196951e-01 -1.999588e-01
## pos_28_pd                            -0.447287370 -2.417102e-01 -3.613312e-02
## Time_Period_ID:RegionMidwest          0.080338552  9.415909e-02  1.079796e-01
## Time_Period_ID:RegionNortheast        0.069818688  1.019535e-01  1.340884e-01
## Time_Period_ID:RegionSouth            0.083574420  9.536909e-02  1.071638e-01
## Time_Period_ID:RegionWest             0.053542316  6.822423e-02  8.290614e-02
## RegionMidwest:I(Time_Period_ID^2)    -0.001451647 -1.007126e-03 -5.626048e-04
## RegionNortheast:I(Time_Period_ID^2)  -0.002291061 -1.307197e-03 -3.233335e-04
## RegionSouth:I(Time_Period_ID^2)      -0.001659722 -1.300744e-03 -9.417655e-04
## RegionWest:I(Time_Period_ID^2)       -0.001261285 -7.722850e-04 -2.832846e-04
##                                          sd_coef
## (Intercept)                         0.0591125963
## StateAlaska                         0.0980937358
## StateArizona                        0.0856380746
## StateArkansas                       0.0704517920
## StateCalifornia                     0.1082198212
## StateColorado                       0.0870205879
## StateConnecticut                    0.1427041563
## StateDelaware                       0.0745042337
## StateFlorida                        0.0646486677
## StateGeorgia                        0.0633389907
## StateHawaii                         0.0889144717
## StateIdaho                          0.0869241826
## StateIllinois                       0.0937174383
## StateIndiana                        0.0857740957
## StateIowa                           0.0878160113
## StateKansas                         0.0791998658
## StateKentucky                       0.0561822461
## StateLouisiana                      0.0640083118
## StateMaine                          0.1452253463
## StateMaryland                       0.1003322239
## StateMassachusetts                  0.1930367266
## StateMichigan                       0.0792533080
## StateMinnesota                      0.0850390486
## StateMississippi                    0.0595015478
## StateMissouri                       0.0754939251
## StateMontana                        0.0880898755
## StateNebraska                       0.0810715098
## StateNevada                         0.0869328287
## StateNew Hampshire                  0.1308072714
## StateNew Jersey                     0.1471168423
## StateNew Mexico                     0.1022155002
## StateNew York                       0.1342040191
## StateNorth Carolina                 0.0526555213
## StateNorth Dakota                   0.1187351952
## StateOhio                           0.0937984719
## StateOklahoma                       0.0558230933
## StateOregon                         0.0867209075
## StatePennsylvania                   0.1289385229
## StateRhode Island                   0.2368055524
## StateSouth Carolina                 0.0604811417
## StateSouth Dakota                   0.0955345685
## StateTennessee                      0.0536825146
## StateTexas                          0.0641256209
## StateUtah                           0.1272370778
## StateVermont                        0.1465865198
## StateVirginia                       0.0608131420
## StateWashington                     0.0875656638
## StateWest Virginia                  0.0913256806
## StateWisconsin                      0.0772307909
## StateWyoming                        0.0989810256
## Naloxone_Pharmacy_Yes_Redefined     0.0544409262
## Naloxone_Pharmacy_No_Redefined      0.0607950298
## Medical_Marijuana_Redefined         0.0550528231
## Recreational_Marijuana_Redefined    0.0705778840
## GSL_Redefined                       0.0513299618
## PDMP_Redefined                      0.0280989900
## Medicaid_Expansion_Redefined        0.0485987258
## pos_0_pd                            0.0451011650
## pos_1_pd                            0.0497750254
## pos_2_pd                            0.0410822608
## pos_3_pd                            0.0417772160
## pos_4_pd                            0.0401321892
## pos_5_pd                            0.0442204321
## pos_6_pd                            0.0486022545
## pos_7_pd                            0.0520225363
## pos_8_pd                            0.0475373944
## pos_9_pd                            0.0551558564
## pos_10_pd                           0.0594827329
## pos_11_pd                           0.0541110882
## pos_12_pd                           0.0631923413
## pos_13_pd                           0.0866967517
## pos_14_pd                           0.0927114176
## pos_15_pd                           0.0649594367
## pos_16_pd                           0.0723656426
## pos_17_pd                           0.0763290368
## pos_18_pd                           0.0836618714
## pos_19_pd                           0.0817260892
## pos_20_pd                           0.0904369243
## pos_21_pd                           0.1202133702
## pos_22_pd                           0.1342290536
## pos_23_pd                           0.1284409881
## pos_24_pd                           0.1052828919
## pos_25_pd                           0.1044383616
## pos_26_pd                           0.1315896356
## pos_27_pd                           0.1121103525
## pos_28_pd                           0.1048862874
## Time_Period_ID:RegionMidwest        0.0070512967
## Time_Period_ID:RegionNortheast      0.0163953295
## Time_Period_ID:RegionSouth          0.0060176879
## Time_Period_ID:RegionWest           0.0074907706
## RegionMidwest:I(Time_Period_ID^2)   0.0002267965
## RegionNortheast:I(Time_Period_ID^2) 0.0005019713
## RegionSouth:I(Time_Period_ID^2)     0.0001831521
## RegionWest:I(Time_Period_ID^2)      0.0002494900

9.7.2 Plot Results

#plot the coefficients for the periods before and after the intervention with 95% CI
plot_post_tx_log_fixed_lin_time_subset <- sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset %>%
  mutate(term = rownames(sensitivity_anlys_post_tx_sd_and_ci_log_fixed_lin_time_subset)) %>%
  dplyr::select(term, coef_values, lb_coef, ub_coef) %>%
  filter(term %in% c(sapply(0:(max(data_subset$Time_Period_ID) - 
                              min(merged_main_time_data_int$intervention_time_id, na.rm = TRUE)), 
                                   function(x){paste("pos_", x, "_pd", sep = "")}))) 
colnames(plot_post_tx_log_fixed_lin_time_subset) <- c("term", "estimate", "conf.low", "conf.high")
plot_post_tx_log_fixed_lin_time_subset$num_states_subset <- sapply(plot_post_tx_log_fixed_lin_time_subset$term, function(x){sum(sensitivity_anlys_event_study_data[,x])})

plot_post_tx_data_lin_time <- merge(plot_post_tx_log_fixed_lin_time, plot_post_tx_log_fixed_lin_time_subset, 
                           by = "term", all.x = TRUE)
plot_post_tx_data_lin_time$term <- factor(plot_post_tx_data_lin_time$term, 
                                                     levels = sapply(0:39, function(x){paste("pos_", x, "_pd", sep = "")}))
ggplot(plot_post_tx_data_lin_time, aes(x = term)) +  
  geom_point(plot_post_tx_data_lin_time, mapping = aes(y = estimate.y, color = "subset data")) + 
  geom_pointrange(plot_post_tx_data_lin_time, 
                  mapping = aes(x = term, y = estimate.y, ymin = conf.low.y, ymax = conf.high.y, color = "subset data"),
                  fatten = 1, alpha = .5) + 
  geom_point(plot_post_tx_data_lin_time, mapping = aes(y = estimate.x, color = "full data")) + 
  geom_pointrange(plot_post_tx_data_lin_time, 
                  mapping = aes(x = term, y = estimate.x, ymin = conf.low.x, ymax = conf.high.x, color = "full data"),
                  fatten = 1, alpha = .5) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.background = element_blank(), axis.line = element_line(colour = "black"), 
        axis.text.x = element_text(angle = 45, size = 4),
        legend.position = "bottom") +
  geom_hline(aes(yintercept = 0), linetype = "dashed") +
  labs(y = "Time Periods", x = "Coefficients and 95% Confidence Intervals", 
       title = "Coefficient of Pre-Intervention and Post-Intervention Periods",
       color = "Full Data or Subset Times") 

9.8 Analysis With Only Periods After Treatment

#run the gam model
sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time<-lm(log(prop_dead)~ State +
                                           Time_Period_ID:Region  +
                                           I(Time_Period_ID^2):Region + 
                                           Naloxone_Pharmacy_Yes_Redefined +
                                           Naloxone_Pharmacy_No_Redefined +
                                           Medical_Marijuana_Redefined +
                                           Recreational_Marijuana_Redefined +
                                           GSL_Redefined +
                                           PDMP_Redefined +
                                           Medicaid_Expansion_Redefined +
                                             time_after_tx,
                                         data = sensitivity_anlys_event_study_data_lin_post_tx)
summary(sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time)
## 
## Call:
## lm(formula = log(prop_dead) ~ State + Time_Period_ID:Region + 
##     I(Time_Period_ID^2):Region + Naloxone_Pharmacy_Yes_Redefined + 
##     Naloxone_Pharmacy_No_Redefined + Medical_Marijuana_Redefined + 
##     Recreational_Marijuana_Redefined + GSL_Redefined + PDMP_Redefined + 
##     Medicaid_Expansion_Redefined + time_after_tx, data = sensitivity_anlys_event_study_data_lin_post_tx)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.03249 -0.13280  0.01456  0.15581  1.17227 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                         -1.080e+01  5.893e-02 -183.313  < 2e-16 ***
## StateAlaska                          3.318e-01  8.851e-02    3.749 0.000183 ***
## StateArizona                         5.175e-01  8.518e-02    6.074 1.49e-09 ***
## StateArkansas                       -5.463e-01  6.756e-02   -8.085 1.08e-15 ***
## StateCalifornia                      2.490e-01  9.141e-02    2.724 0.006513 ** 
## StateColorado                        2.392e-01  8.844e-02    2.705 0.006899 ** 
## StateConnecticut                     1.164e-01  8.948e-02    1.301 0.193483    
## StateDelaware                        1.012e-01  6.911e-02    1.465 0.143128    
## StateFlorida                         4.647e-01  6.956e-02    6.680 3.11e-11 ***
## StateGeorgia                         1.731e-01  7.051e-02    2.455 0.014181 *  
## StateHawaii                         -1.928e-01  8.769e-02   -2.198 0.028040 *  
## StateIdaho                           9.113e-02  8.584e-02    1.062 0.288569    
## StateIllinois                        1.185e-01  8.729e-02    1.358 0.174762    
## StateIndiana                        -6.576e-02  8.594e-02   -0.765 0.444253    
## StateIowa                           -7.200e-01  8.589e-02   -8.383  < 2e-16 ***
## StateKansas                         -3.349e-01  8.529e-02   -3.926 8.94e-05 ***
## StateKentucky                        6.487e-01  6.745e-02    9.618  < 2e-16 ***
## StateLouisiana                       4.248e-01  6.717e-02    6.324 3.16e-10 ***
## StateMaine                          -5.379e-02  9.206e-02   -0.584 0.559109    
## StateMaryland                       -1.408e+00  6.933e-02  -20.307  < 2e-16 ***
## StateMassachusetts                  -1.937e-01  8.946e-02   -2.165 0.030519 *  
## StateMichigan                       -6.126e-02  8.659e-02   -0.707 0.479357    
## StateMinnesota                      -7.856e-01  8.730e-02   -9.000  < 2e-16 ***
## StateMississippi                    -1.301e-01  6.702e-02   -1.942 0.052301 .  
## StateMissouri                        7.795e-02  8.694e-02    0.897 0.370048    
## StateMontana                        -7.602e-02  8.751e-02   -0.869 0.385093    
## StateNebraska                       -1.047e+00  8.652e-02  -12.105  < 2e-16 ***
## StateNevada                          7.862e-01  8.807e-02    8.927  < 2e-16 ***
## StateNew Hampshire                   3.425e-03  8.914e-02    0.038 0.969350    
## StateNew Jersey                      7.823e-02  9.041e-02    0.865 0.386993    
## StateNew Mexico                      8.722e-01  8.763e-02    9.953  < 2e-16 ***
## StateNew York                       -2.386e-01  8.918e-02   -2.676 0.007517 ** 
## StateNorth Carolina                  2.766e-01  6.670e-02    4.148 3.51e-05 ***
## StateNorth Dakota                   -1.331e+00  8.591e-02  -15.495  < 2e-16 ***
## StateOhio                            5.169e-01  8.823e-02    5.859 5.46e-09 ***
## StateOklahoma                        4.199e-01  6.712e-02    6.257 4.83e-10 ***
## StateOregon                         -5.379e-02  8.840e-02   -0.608 0.542933    
## StatePennsylvania                    6.265e-01  9.247e-02    6.776 1.64e-11 ***
## StateRhode Island                   -4.734e-01  8.970e-02   -5.278 1.46e-07 ***
## StateSouth Carolina                  1.221e-01  6.733e-02    1.813 0.069960 .  
## StateSouth Dakota                   -1.247e+00  8.651e-02  -14.417  < 2e-16 ***
## StateTennessee                       4.651e-01  6.626e-02    7.018 3.10e-12 ***
## StateTexas                           1.377e-01  6.958e-02    1.979 0.047941 *  
## StateUtah                            2.581e-01  8.596e-02    3.003 0.002708 ** 
## StateVermont                        -3.283e-01  8.947e-02   -3.670 0.000249 ***
## StateVirginia                        6.504e-02  6.746e-02    0.964 0.335108    
## StateWashington                      2.883e-01  8.889e-02    3.243 0.001202 ** 
## StateWest Virginia                   7.370e-01  6.759e-02   10.903  < 2e-16 ***
## StateWisconsin                      -4.138e-02  8.598e-02   -0.481 0.630407    
## StateWyoming                         2.680e-01  8.548e-02    3.135 0.001743 ** 
## Naloxone_Pharmacy_Yes_Redefined      6.423e-02  3.878e-02    1.656 0.097821 .  
## Naloxone_Pharmacy_No_Redefined       1.637e-02  3.815e-02    0.429 0.667946    
## Medical_Marijuana_Redefined          2.219e-01  3.064e-02    7.243 6.29e-13 ***
## Recreational_Marijuana_Redefined    -7.615e-02  4.826e-02   -1.578 0.114733    
## GSL_Redefined                        6.153e-02  3.118e-02    1.974 0.048566 *  
## PDMP_Redefined                      -1.809e-01  2.458e-02   -7.360 2.70e-13 ***
## Medicaid_Expansion_Redefined         7.524e-02  2.948e-02    2.552 0.010783 *  
## time_after_tx                       -1.539e-02  1.833e-03   -8.398  < 2e-16 ***
## Time_Period_ID:RegionMidwest         8.246e-02  5.098e-03   16.175  < 2e-16 ***
## Time_Period_ID:RegionNortheast       7.030e-02  5.887e-03   11.943  < 2e-16 ***
## Time_Period_ID:RegionSouth           7.655e-02  4.563e-03   16.777  < 2e-16 ***
## Time_Period_ID:RegionWest            6.194e-02  5.042e-03   12.284  < 2e-16 ***
## RegionMidwest:I(Time_Period_ID^2)   -7.001e-04  1.283e-04   -5.455 5.52e-08 ***
## RegionNortheast:I(Time_Period_ID^2) -3.013e-04  1.491e-04   -2.021 0.043394 *  
## RegionSouth:I(Time_Period_ID^2)     -7.078e-04  1.182e-04   -5.986 2.56e-09 ***
## RegionWest:I(Time_Period_ID^2)      -6.997e-04  1.304e-04   -5.366 9.00e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2959 on 1934 degrees of freedom
## Multiple R-squared:  0.8424, Adjusted R-squared:  0.8371 
## F-statistic: 159.1 on 65 and 1934 DF,  p-value: < 2.2e-16

9.8.1 Sandwich Estimator

#compute the full dataset including basis functions
full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_fixed_lin_time <-
  model.matrix(sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time)

#estimate the 95% CI and SD
coefficient_values_sensitivity_anlys_lin_post_tx_log_fixed_lin_time <- coef(sensitivity_anlys_lin_post_tx_model_log_fixed_lin_time)

sensitivity_anlys_lin_post_tx_sd_and_ci_log_fixed_lin_time <-
  compute_sd_and_CI((full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_fixed_lin_time), 
                                                         log(sensitivity_anlys_event_study_data$prop_dead),
                                                         coefficient_values_sensitivity_anlys_lin_post_tx_log_fixed_lin_time,
                    p = ncol(full_df_w_basis_functions_sensitivity_anlys_lin_post_tx_log_fixed_lin_time) - 50)
sensitivity_anlys_lin_post_tx_sd_and_ci_log_fixed_lin_time
##                                           lb_coef   coef_values       ub_coef
## (Intercept)                         -11.032395000 -1.080239e+01 -1.057239e+01
## StateAlaska                           0.016119143  3.318378e-01  6.475564e-01
## StateArizona                          0.227468105  5.174508e-01  8.074335e-01
## StateArkansas                        -0.863335048 -5.462754e-01 -2.292158e-01
## StateCalifornia                      -0.096482075  2.489906e-01  5.944634e-01
## StateColorado                        -0.085686088  2.391839e-01  5.640538e-01
## StateConnecticut                     -0.283445482  1.163972e-01  5.162399e-01
## StateDelaware                        -0.174119494  1.012298e-01  3.765791e-01
## StateFlorida                          0.201896555  4.646892e-01  7.274818e-01
## StateGeorgia                         -0.091851419  1.731041e-01  4.380595e-01
## StateHawaii                          -0.511866569 -1.927779e-01  1.263109e-01
## StateIdaho                           -0.204980318  9.112647e-02  3.872333e-01
## StateIllinois                        -0.238825672  1.185006e-01  4.758269e-01
## StateIndiana                         -0.450526951 -6.576075e-02  3.190055e-01
## StateIowa                            -1.064890868 -7.199910e-01 -3.750911e-01
## StateKansas                          -0.662085495 -3.348702e-01 -7.654874e-03
## StateKentucky                         0.372653717  6.487138e-01  9.247738e-01
## StateLouisiana                        0.158121609  4.247528e-01  6.913840e-01
## StateMaine                           -0.467240181 -5.378727e-02  3.596656e-01
## StateMaryland                        -1.743134907 -1.407828e+00 -1.072521e+00
## StateMassachusetts                   -0.757246301 -1.936757e-01  3.698950e-01
## StateMichigan                        -0.439494246 -6.126213e-02  3.169700e-01
## StateMinnesota                       -1.141741473 -7.856417e-01 -4.295420e-01
## StateMississippi                     -0.397788973 -1.301446e-01  1.374998e-01
## StateMissouri                        -0.272918897  7.795126e-02  4.288214e-01
## StateMontana                         -0.399997560 -7.602383e-02  2.479499e-01
## StateNebraska                        -1.389690270 -1.047361e+00 -7.050309e-01
## StateNevada                           0.459143786  7.862456e-01  1.113347e+00
## StateNew Hampshire                   -0.415258494  3.425310e-03  4.221091e-01
## StateNew Jersey                      -0.324125945  7.822777e-02  4.805815e-01
## StateNew Mexico                       0.564941559  8.721992e-01  1.179457e+00
## StateNew York                        -0.657431192 -2.386233e-01  1.801846e-01
## StateNorth Carolina                   0.031729340  2.766402e-01  5.215511e-01
## StateNorth Dakota                    -1.698467508 -1.331114e+00 -9.637606e-01
## StateOhio                             0.143560454  5.169380e-01  8.903155e-01
## StateOklahoma                         0.133389278  4.199129e-01  7.064365e-01
## StateOregon                          -0.375097488 -5.379034e-02  2.675168e-01
## StatePennsylvania                     0.203945754  6.265481e-01  1.049150e+00
## StateRhode Island                    -1.128235679 -4.734177e-01  1.814002e-01
## StateSouth Carolina                  -0.155208441  1.220894e-01  3.993873e-01
## StateSouth Dakota                    -1.633177042 -1.247205e+00 -8.612334e-01
## StateTennessee                        0.201040214  4.650537e-01  7.290673e-01
## StateTexas                           -0.120222722  1.377115e-01  3.956457e-01
## StateUtah                            -0.096631293  2.581386e-01  6.129085e-01
## StateVermont                         -0.739270544 -3.283355e-01  8.259958e-02
## StateVirginia                        -0.180958424  6.503933e-02  3.110371e-01
## StateWashington                      -0.040520561  2.882924e-01  6.171053e-01
## StateWest Virginia                    0.421412780  7.369630e-01  1.052513e+00
## StateWisconsin                       -0.373393925 -4.137857e-02  2.906368e-01
## StateWyoming                         -0.041192639  2.679994e-01  5.771914e-01
## Naloxone_Pharmacy_Yes_Redefined      -0.094785812  6.422503e-02  2.232359e-01
## Naloxone_Pharmacy_No_Redefined       -0.139632361  1.636668e-02  1.723657e-01
## Medical_Marijuana_Redefined           0.047111334  2.219211e-01  3.967308e-01
## Recreational_Marijuana_Redefined     -0.407922621 -7.614735e-02  2.556279e-01
## GSL_Redefined                        -0.076199957  6.153342e-02  1.992668e-01
## PDMP_Redefined                       -0.284064894 -1.808890e-01 -7.771309e-02
## Medicaid_Expansion_Redefined         -0.070853004  7.523711e-02  2.213272e-01
## time_after_tx                        -0.024856265 -1.539237e-02 -5.928480e-03
## Time_Period_ID:RegionMidwest          0.059532671  8.245797e-02  1.053833e-01
## Time_Period_ID:RegionNortheast        0.032505859  7.030490e-02  1.081039e-01
## Time_Period_ID:RegionSouth            0.057796075  7.654703e-02  9.529798e-02
## Time_Period_ID:RegionWest             0.043675612  6.193861e-02  8.020160e-02
## RegionMidwest:I(Time_Period_ID^2)    -0.001365405 -7.001224e-04 -3.483966e-05
## RegionNortheast:I(Time_Period_ID^2)  -0.001440955 -3.012815e-04  8.383919e-04
## RegionSouth:I(Time_Period_ID^2)      -0.001259972 -7.078005e-04 -1.556288e-04
## RegionWest:I(Time_Period_ID^2)       -0.001250245 -6.996678e-04 -1.490906e-04
##                                          sd_coef
## (Intercept)                         0.1173490481
## StateAlaska                         0.1610809373
## StateArizona                        0.1479503602
## StateArkansas                       0.1617651094
## StateCalifornia                     0.1762615891
## StateColorado                       0.1657499715
## StateConnecticut                    0.2040013847
## StateDelaware                       0.1404843224
## StateFlorida                        0.1340778593
## StateGeorgia                        0.1351813649
## StateHawaii                         0.1628003639
## StateIdaho                          0.1510748900
## StateIllinois                       0.1823093222
## StateIndiana                        0.1963092883
## StateIowa                           0.1759693219
## StateKansas                         0.1669465869
## StateKentucky                       0.1408469601
## StateLouisiana                      0.1360363128
## StateMaine                          0.2109453620
## StateMaryland                       0.1710749459
## StateMassachusetts                  0.2875360375
## StateMichigan                       0.1929755715
## StateMinnesota                      0.1816835457
## StateMississippi                    0.1365532677
## StateMissouri                       0.1790153884
## StateMontana                        0.1652927169
## StateNebraska                       0.1746580152
## StateNevada                         0.1668886967
## StateNew Hampshire                  0.2136141855
## StateNew Jersey                     0.2052825074
## StateNew Mexico                     0.1567640963
## StateNew York                       0.2136775066
## StateNorth Carolina                 0.1249545377
## StateNorth Dakota                   0.1874252275
## StateOhio                           0.1904987489
## StateOklahoma                       0.1461855086
## StateOregon                         0.1639322162
## StatePennsylvania                   0.2156134313
## StateRhode Island                   0.3340907852
## StateSouth Carolina                 0.1414785137
## StateSouth Dakota                   0.1969244111
## StateTennessee                      0.1347007823
## StateTexas                          0.1315990905
## StateUtah                           0.1810050386
## StateVermont                        0.2096607458
## StateVirginia                       0.1255090597
## StateWashington                     0.1677617090
## StateWest Virginia                  0.1609949936
## StateWisconsin                      0.1693955894
## StateWyoming                        0.1577510213
## Naloxone_Pharmacy_Yes_Redefined     0.0811279823
## Naloxone_Pharmacy_No_Redefined      0.0795913458
## Medical_Marijuana_Redefined         0.0891886370
## Recreational_Marijuana_Redefined    0.1692730984
## GSL_Redefined                       0.0702721302
## PDMP_Redefined                      0.0526407657
## Medicaid_Expansion_Redefined        0.0745357728
## time_after_tx                       0.0048285167
## Time_Period_ID:RegionMidwest        0.0116965829
## Time_Period_ID:RegionNortheast      0.0192852249
## Time_Period_ID:RegionSouth          0.0095668113
## Time_Period_ID:RegionWest           0.0093178545
## RegionMidwest:I(Time_Period_ID^2)   0.0003394300
## RegionNortheast:I(Time_Period_ID^2) 0.0005814660
## RegionSouth:I(Time_Period_ID^2)     0.0002817203
## RegionWest:I(Time_Period_ID^2)      0.0002809067